Edit Profile (opens in new tab) Sogge, Christopher D. Compute Distance To: Compute Author ID: sogge.christopher-d Published as: Sogge, Christopher D.; Sogge, C. D.; Sogge, Christopher; Sogge, Chris D. more...less External Links: MGP · Wikidata · GND · IdRef Documents Indexed: 121 Publications since 1985, including 6 Books 1 Contribution as Editor · 2 Further Contributions Co-Authors: 55 Co-Authors with 90 Joint Publications 1,857 Co-Co-Authors all top 5 Co-Authors 33 single-authored 17 Smith, Hart F. 11 Metcalfe, Jason L. 10 Blair, Matthew D. 10 Zelditch, Steve 7 Lindblad, Hans 6 Wang, Chengbo 5 Seeger, Andreas 4 Keel, Markus 4 Kenig, Carlos Eduardo 4 Sire, Yannick 4 Stein, Elias Menachem 3 Nakamura, Makoto 3 Xi, Yakun 2 Beltran, David 2 Chen, Xuehua 2 Christ, Michael 2 Fefferman, Charles Louis 2 Hickman, Jonathan 2 Huang, Xiaoqi 2 Journé, Jean-Lin 2 Lanzani, Loredana 2 Minicozzi, William Philip II 2 Mockenhaupt, Gerd 2 Nagel, Alexander 2 Phong, Duong Hong 2 Pierce, Lillian B. 2 Ricci, Fulvio 2 Ruiz, Alberto 2 Soffer, Avraham 2 Tao, Terence 2 Wainger, Stephen 2 Zhang, Junyong 2 Zhou, Yi 1 Barceló, Bartolomé 1 Beckner, William 1 Bourgain, Jean 1 Christ, F. M. 1 Dafni, Galia 1 Du, Yi 1 Georgiev, Vladimir S. 1 Hezari, Hamid 1 Hidano, Kunio 1 Huang, Shanlin 1 Ionescu, Alex 1 Ionescu, Alexandru D. 1 Kearn, Vickie 1 Knapp, Anthony William 1 Krantz, Steven George 1 Lu, Jianfeng 1 Magyar, Akos 1 Miao, Changxing 1 Mirek, Mariusz 1 Nahmod, Andrea R. 1 Oberlin, Daniel M. 1 Pan, Yibiao 1 Rothschild, Linda Preiss 1 Schlag, Wilhelm 1 Shahidi, Freydoon 1 Shakarchi, Rami 1 Shao, Peng 1 Shokurov, Vyacheslav Vladimirovich 1 Stein, Jeremy C. 1 Stein, Karen 1 Steinerberger, Stefan 1 Stewart, Ann Ann 1 Street, Brian 1 Tohaneanu, Mihai 1 Toth, John Andrew 1 Wang, Xing 1 Widom, Harold 1 Xu, Hang 1 Yang, Jianwei 1 Yao, Xiaohua 1 Zhang, Cheng 1 Zhang, Xiaoyi 1 Zheng, Shijun 1 Zhou, Zhengfang 1 Zhu, Jiuyi all top 5 Serials 9 Mathematical Research Letters 8 Communications in Partial Differential Equations 6 American Journal of Mathematics 6 Duke Mathematical Journal 6 Inventiones Mathematicae 6 Journal of Functional Analysis 5 Proceedings of the American Mathematical Society 5 Transactions of the American Mathematical Society 5 Journal of the American Mathematical Society 4 The Journal of Geometric Analysis 3 Communications in Mathematical Physics 3 Journal d’Analyse Mathématique 3 Mathematische Annalen 3 Annals of Mathematics. Second Series 3 Cambridge Tracts in Mathematics 3 Analysis & PDE 2 Revista Matemática Iberoamericana 2 Bulletin of the American Mathematical Society. New Series 2 Discrete and Continuous Dynamical Systems 1 Communications on Pure and Applied Mathematics 1 Arkiv för Matematik 1 Acta Mathematica 1 Advances in Mathematics 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Colloquium Mathematicum 1 Illinois Journal of Mathematics 1 Indiana University Mathematics Journal 1 Journal of Differential Equations 1 Journal of Differential Geometry 1 Japanese Journal of Mathematics. New Series 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 Tohoku Mathematical Journal. Second Series 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Forum Mathematicum 1 SIAM Journal on Mathematical Analysis 1 Notices of the American Mathematical Society 1 Journées Équations aux Dérivées Partielles (Saint-Jean-de-Monts) 1 Séminaire Équations aux Dérivées Partielles 1 Journal of the European Mathematical Society (JEMS) 1 Annals of Mathematics Studies 1 Contemporary Mathematics 1 RIMS Kôkyûroku Bessatsu 1 Cambridge Journal of Mathematics all top 5 Fields 98 Partial differential equations (35-XX) 52 Global analysis, analysis on manifolds (58-XX) 37 Harmonic analysis on Euclidean spaces (42-XX) 9 Operator theory (47-XX) 7 Differential geometry (53-XX) 3 Several complex variables and analytic spaces (32-XX) 2 History and biography (01-XX) 2 Abstract harmonic analysis (43-XX) 2 Functional analysis (46-XX) 1 General and overarching topics; collections (00-XX) 1 Real functions (26-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral transforms, operational calculus (44-XX) 1 Mechanics of deformable solids (74-XX) 1 Fluid mechanics (76-XX) 1 Optics, electromagnetic theory (78-XX) 1 Quantum theory (81-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 111 Publications have been cited 2,966 times in 1,515 Documents Cited by ▼ Year ▼ Fourier integrals in classical analysis. Zbl 0783.35001Sogge, Christopher D. 198 1993 On existence and scattering with minimal regularity for semilinear wave equations. Zbl 0846.35085Lindblad, Hans; Sogge, Christopher D. 165 1995 Uniform Sobolev inequalities and unique continuation for second order constant coefficient differential operators. Zbl 0644.35012Kenig, C. E.; Ruiz, A.; Sogge, C. D. 141 1987 Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds. Zbl 0641.46011Sogge, Christopher D. 122 1988 Weighted Strichartz estimates and global existence for semilinear wave equations. Zbl 0893.35075Georgiev, Vladimir; Lindblad, Hans; Sogge, Christopher D. 122 1997 Decay estimates for Schrödinger operators. Zbl 0743.35008Journé, J.-L.; Soffer, A.; Sogge, C. D. 114 1991 Global Strichartz estimates for nontrapping perturbations of the Laplacian. Zbl 0972.35014Smith, Hart F.; Sogge, Christopher D. 88 2000 Regularity properties of Fourier integral operators. Zbl 0754.58037Seeger, Andreas; Sogge, Christopher D.; Stein, Elias M. 85 1991 Lectures on nonlinear wave equations. Zbl 1089.35500Sogge, Christopher D. 82 1995 Oscillatory integrals and spherical harmonics. Zbl 0636.42018Sogge, Christopher D. 73 1986 Local smoothing of Fourier integral operators and Carleson-Sjölin estimates. Zbl 0776.58037Mockenhaupt, Gerd; Seeger, Andreas; Sogge, Christopher D. 73 1993 Long-time existence for small amplitude semilinear wave equations. Zbl 0869.35064Lindblad, Hans; Sogge, Christopher D. 68 1996 Averages of functions over hypersurfaces in \(\mathbb R^n\). Zbl 0626.42009Sogge, Christopher D.; Stein, Elias M. 58 1985 Almost global existence for some semilinear wave equations. Zbl 1031.35107Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 53 2002 Wave front sets, local smoothing and Bourgain’s circular maximal theorem. Zbl 0759.42016Mockenhaupt, Gerd; Seeger, Andreas; Sogge, Christopher D. 52 1992 Lectures on nonlinear wave equations. 2nd ed. Zbl 1165.35001Sogge, Christopher D. 51 2008 Almost global existence for quasilinear wave equations in three space dimensions. Zbl 1055.35075Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 51 2004 On the convergence of Riesz means on compact manifolds. Zbl 0653.35068Sogge, Christopher D. 50 1987 Long-time existence of quasilinear wave equations exterior to star-shaped obstacles via energy methods. Zbl 1162.35052Metcalfe, Jason; Sogge, Christopher D. 44 2006 Riemannian manifolds with maximal eigenfunction growth. Zbl 1018.58010Sogge, Christopher D.; Zelditch, Steve 43 2002 The weak type \(L^ 1\) convergence of eigenfunction expansions for pseudodifferential operators. Zbl 0678.35096Christ, F. M.; Sogge, C. D. 40 1988 Strichartz estimates for the wave equation on manifolds with boundary. Zbl 1198.58012Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 40 2009 On the boundedness of functions of (pseudo-) differential operators on compact manifolds. Zbl 0698.35169Seeger, A.; Sogge, C. D. 40 1989 Hangzhou lectures on eigenfunctions of the Laplacian. Zbl 1312.58001Sogge, Christopher D. 39 2014 Propagation of singularities and maximal functions in the plane. Zbl 0754.35004Sogge, Christopher D. 39 1991 On the \(L^p\) norm of spectral clusters for compact manifolds with boundary. Zbl 1189.58017Smith, Hart F.; Sogge, Christopher D. 37 2007 On the critical semilinear wave equation outside convex obstacles. Zbl 0860.35081Smith, Hart F.; Sogge, Christopher D. 35 1995 On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles. Zbl 1193.35100Hidano, Kunio; Metcalfe, Jason; Smith, Hart F.; Sogge, Christopher D.; Zhou, Yi 35 2010 Global existence of null-form wave equations in exterior domains. Zbl 1138.35065Metcalfe, Jason; Sogge, Christopher D. 30 2007 Strong uniqueness theorems for second order elliptic differential equations. Zbl 0734.35012Sogge, Christopher D. 29 1990 Bounds for eigenfunctions of differential operators. Zbl 0703.35133Seeger, A.; Sogge, C. D. 28 1989 Lower bounds on the Hausdorff measure of nodal sets. Zbl 1242.58017Sogge, Christopher D.; Zelditch, Steve 28 2011 The Strauss conjecture on Kerr black hole backgrounds. Zbl 1295.35327Lindblad, Hans; Metcalfe, Jason; Sogge, Christopher D.; Tohaneanu, Mihai; Wang, Chengbo 27 2014 Global existence for a quasilinear wave equation outside of star-shaped domains. Zbl 1001.35087Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 27 2002 Hyperbolic trapped rays and global existence of quasilinear wave equations. Zbl 1077.35083Metcalfe, Jason; Sogge, Christopher D. 25 2005 Fourier integrals in classical analysis. 2nd edition. Zbl 1361.35005Sogge, Christopher D. 25 2017 On Strichartz estimates for Schrödinger operators in compact manifolds with boundary. Zbl 1169.35012Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 23 2008 Kakeya-Nikodym averages and \(L^p\)-norms of eigenfunctions. Zbl 1234.35156Sogge, Christopher D. 23 2011 About the blowup of quasimodes on Riemannian manifolds. Zbl 1214.58012Sogge, Christopher D.; Toth, John A.; Zelditch, Steve 22 2011 Strichartz estimates for Dirichlet-wave equations in two dimensions with applications. Zbl 1246.35052Smith, Hart F.; Sogge, Christopher D.; Wang, Chengbo 22 2012 Concerning the wave equation on asymptotically Euclidean manifolds. Zbl 1231.35030Sogge, Christopher D.; Wang, Chengbo 21 2010 Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions. Zbl 1209.35083Du, Yi; Metcalfe, Jason; Sogge, Christopher D.; Zhou, Yi 21 2008 Local smoothing estimates related to the circular maximal theorem. Zbl 0877.42006Schlag, Wilhelm; Sogge, Christopher D. 20 1997 A unique continuation theorem for second order parabolic differential operators. Zbl 0704.35016Sogge, C. D. 19 1990 A natural lower bound for the size of nodal sets. Zbl 1329.35224Hezari, Hamid; Sogge, Christopher D. 19 2012 Eigenfunction and Bochner Riesz estimates on manifolds with boundary. Zbl 1017.58016Sogge, Christopher D. 18 2002 Lower bounds on the Hausdorff measure of nodal sets. II. Zbl 1283.58020Sogge, Christopher D.; Zelditch, Steve 17 2012 Averages over hypersurfaces. Smoothness of generalized Radon transforms. Zbl 0695.42012Sogge, C. D.; Stein, Elias M. 17 1990 Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary. Zbl 1262.58015Blair, Matthew D.; Smith, Hart F.; Sogge, Chris D. 17 2012 On \(L^p\)-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds. Zbl 1396.58025Bourgain, Jean; Shao, Peng; Sogge, Christopher D.; Yao, Xiaohua 16 2015 Global existence for nonlinear wave equations with multiple speeds. Zbl 1052.35133Sogge, Christopher D. 16 2003 On eigenfunction restriction estimates and \(L^4\)-bounds for compact surfaces with nonpositive curvature. Zbl 1307.58013Sogge, Christopher D.; Zelditch, Steve 15 2014 A note on unique continuation for Schrödinger’s operator. Zbl 0661.35056Kenig, Carlos E.; Sogge, Christopher D. 14 1988 Weighted Sobolev inequalities and unique continuation for the Laplacian plus lower order terms. Zbl 0689.35015Barcelo, B.; Kenig, C. E.; Ruiz, A.; Sogge, C. D. 14 1988 Oscillatory integrals associated to folding canonical relations. Zbl 0746.58076Pan, Yibiao; Sogge, Christopher D. 14 1990 Negative results for Nikodym maximal functions and related oscillatory integrals in curved space. Zbl 0884.42016Minicozzi, William P. II; Sogge, Christopher D. 14 1997 Averages over hypersurfaces. II. Zbl 0656.42012Sogge, Christopher D.; Stein, Elias M. 13 1986 A few endpoint geodesic restriction estimates for eigenfunctions. Zbl 1293.58011Chen, Xuehua; Sogge, Christopher D. 13 2014 Oscillatory integrals and unique continuation for second order elliptic differential equations. Zbl 0703.35027Sogge, Christopher D. 13 1989 Global existence for Dirichlet-wave equations with quadratic nonlinearities in high dimensions. Zbl 1185.35140Metcalfe, Jason; Sogge, Christopher D. 13 2006 Nonlinear hyperbolic equations in infinite homogeneous waveguides. Zbl 1078.35076Metcalfe, Jason; Sogge, Christopher D.; Stewart, Ann Ann 13 2005 Concerning Toponogov’s theorem and logarithmic improvement of estimates of eigenfunctions. Zbl 1394.58016Blair, Matthew D.; Sogge, Christopher D. 13 2018 Focal points and sup-norms of eigenfunctions. Zbl 1361.32011Sogge, Christopher D.; Zelditch, Steve 13 2016 Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition. Zbl 1098.35112Metcalfe, Jason; Nakamura, Makoto; Sogge, Christopher D. 12 2005 Maximal operators associated to hypersurfaces with one nonvanishing principal curvature. Zbl 0880.42011Sogge, Christopher D. 12 1995 Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains. Zbl 1149.35055Metcalfe, Jason; Nakamura, Makoto; Sogge, Christopher D. 12 2005 On Strichartz and eigenfunction estimates for low regularity metrics. Zbl 0832.35018Smith, Hart F.; Sogge, Christopher D. 12 1994 Localized \(L^{p}\)-estimates of eigenfunctions: a note on an article of Hezari and Rivière. Zbl 1331.58036Sogge, Christopher D. 11 2016 On integrals of eigenfunctions over geodesics. Zbl 1321.58023Chen, Xuehua; Sogge, Christopher D. 10 2015 Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds. Zbl 1436.35340Beltran, David; Hickman, Jonathan; Sogge, Christopher D. 10 2020 A sharp restriction theorem for degenerate curves in \(R^ 2\). Zbl 0621.42009Sogge, Christopher D. 9 1987 Concerning Nikodym-type sets in 3-dimensional curved spaces. Zbl 0968.42016Sogge, Christopher D. 9 1999 Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. Zbl 1213.35314Metcalfe, Jason; Sogge, Christopher D. 9 2010 On Kakeya-Nikodym averages, \(L^p\)-norms and lower bounds for nodal sets of eigenfunctions in higher dimensions. Zbl 1330.58023Blair, Matthew D.; Sogge, Christopher D. 9 2015 Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions. Zbl 1321.58029Blair, Matthew D.; Sogge, Christopher D. 8 2015 Concerning \(L^p\) resolvent estimates for simply connected manifolds of constant curvature. Zbl 1303.53052Huang, Shanlin; Sogge, Christopher D. 8 2014 Remarks on global solutions for nonlinear wave equations under the standard null conditions. Zbl 1262.35170Lindblad, Hans; Nakamura, Makoto; Sogge, Christopher D. 8 2013 Improved critical eigenfunction estimates on manifolds of nonpositive curvature. Zbl 1386.58014Sogge, Christopher D. 8 2017 Geodesic period integrals of eigenfunctions on Riemannian surfaces and the Gauss-Bonnet theorem. Zbl 1377.35204Sogge, Christopher D.; Xi, Yakun; Zhang, Cheng 8 2017 Concerning the \(L^4\) norms of typical eigenfunctions on compact surfaces. Zbl 1317.58035Sogge, Christopher D.; Zelditch, Steve 7 2012 Refined and microlocal Kakeya-Nikodym bounds of eigenfunctions in higher dimensions. Zbl 1377.58026Blair, Matthew D.; Sogge, Christopher D. 7 2017 Restriction theorems and semilinear Klein-Gordon equations in \((1+3)\)-dimensions. Zbl 0865.35077Lindblad, Hans; Sogge, Christopher D. 6 1996 Uniqueness in Cauchy problems for hyperbolic differential operators. Zbl 0763.35012Sogge, Christopher D. 6 1992 \(L^ p\) regularity for the wave equation with strictly convex obstacles. Zbl 0805.35169Smith, Hart F.; Sogge, Christopher D. 6 1994 Logarithmic improvements in \(L^{p}\) bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature. Zbl 1428.35248Blair, Matthew D.; Sogge, Christopher D. 6 2019 On global existence for nonlinear wave equations outside of convex obstacles. Zbl 0957.35088Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 5 2000 Focal points and sup-norms of eigenfunctions II: the two-dimensional case. Zbl 1376.32011Sogge, Christopher D.; Zelditch, Steve 5 2016 Lower bounds for interior nodal sets of Steklov eigenfunctions. Zbl 1359.35116Sogge, Christopher D.; Wang, Xing; Zhu, Jiuyi 5 2016 Fourier integrals in classical analysis. Paperback reprint of the hardback edition 1993. Zbl 1143.35002Sogge, Christopher D. 4 2008 Averages over curves with torsion. Zbl 0934.42008Oberlin, Daniel; Smith, Hart F.; Sogge, Christopher D. 4 1998 A note on \(L^p\)-norms of quasi-modes. Zbl 1364.35219Sogge, Christopher D.; Zelditch, Steve 4 2016 On multilinear spectral cluster estimates for manifolds with boundary. Zbl 1146.58019Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 3 2008 On local existence for nonlinear wave equations satisfying variable coefficient null conditions. Zbl 0792.35125Sogge, Christopher D. 3 1993 \(L^ p \to{} L^{p'}\) estimates for time-dependent Schrödinger operators. Zbl 0751.35011Journé, J. L.; Soffer, A.; Sogge, C. D. 3 1990 Sup norms of Cauchy data of eigenfunctions on manifolds with concave boundary. Zbl 1393.35016Sogge, Christopher D.; Zelditch, Steve 3 2017 Approximating pointwise products of Laplacian eigenfunctions. Zbl 1447.35228Lu, Jianfeng; Sogge, Christopher D.; Steinerberger, Stefan 3 2019 On maximal functions associated to hypersurfaces and the Cauchy problem for strictly hyperbolic operators. Zbl 0653.42017Sogge, Christopher D. 2 1987 Remarks on \(L^ 2\) restriction theorems for Riemannian manifolds. Zbl 0681.42009Sogge, C. D. 2 1989 Quasimode, eigenfunction and spectral projection bounds for Schrödinger operators on manifolds with critically singular potentials. Zbl 1472.35257Blair, Matthew D.; Sire, Yannick; Sogge, Christopher D. 2 2021 Smoothing estimates for the wave equation and applications. Zbl 0901.35050Sogge, Christopher D. 2 1995 Quasimode, eigenfunction and spectral projection bounds for Schrödinger operators on manifolds with critically singular potentials. Zbl 1472.35257Blair, Matthew D.; Sire, Yannick; Sogge, Christopher D. 2 2021 Sharp local smoothing estimates for Fourier integral operators. Zbl 07444049Beltran, David; Hickman, Jonathan; Sogge, Christopher D. 1 2021 Variable coefficient Wolff-type inequalities and sharp local smoothing estimates for wave equations on manifolds. Zbl 1436.35340Beltran, David; Hickman, Jonathan; Sogge, Christopher D. 10 2020 Analysis and applications: the mathematical work of Elias Stein. Zbl 1452.32001Fefferman, Charles; Ionescu, Alex; Tao, Terence; Wainger, Stephen 1 2020 Strichartz estimates and Strauss conjecture on non-trapping asymptotically hyperbolic manifolds. Zbl 07269819Sire, Yannick; Sogge, Christopher D.; Wang, Chengbo; Zhang, Junyong 1 2020 Logarithmic improvements in \(L^{p}\) bounds for eigenfunctions at the critical exponent in the presence of nonpositive curvature. Zbl 1428.35248Blair, Matthew D.; Sogge, Christopher D. 6 2019 Approximating pointwise products of Laplacian eigenfunctions. Zbl 1447.35228Lu, Jianfeng; Sogge, Christopher D.; Steinerberger, Stefan 3 2019 The Strauss conjecture on negatively curved backgrounds. Zbl 1428.35231Sire, Yannick; Sogge, Christopher D.; Wang, Chengbo 2 2019 Concerning Toponogov’s theorem and logarithmic improvement of estimates of eigenfunctions. Zbl 1394.58016Blair, Matthew D.; Sogge, Christopher D. 13 2018 On instability of the Nikodym maximal function bounds over Riemannian manifolds. Zbl 1440.42091Sogge, Christopher D.; Xi, Yakun; Xu, Hang 1 2018 Fourier integrals in classical analysis. 2nd edition. Zbl 1361.35005Sogge, Christopher D. 25 2017 Improved critical eigenfunction estimates on manifolds of nonpositive curvature. Zbl 1386.58014Sogge, Christopher D. 8 2017 Geodesic period integrals of eigenfunctions on Riemannian surfaces and the Gauss-Bonnet theorem. Zbl 1377.35204Sogge, Christopher D.; Xi, Yakun; Zhang, Cheng 8 2017 Refined and microlocal Kakeya-Nikodym bounds of eigenfunctions in higher dimensions. Zbl 1377.58026Blair, Matthew D.; Sogge, Christopher D. 7 2017 Sup norms of Cauchy data of eigenfunctions on manifolds with concave boundary. Zbl 1393.35016Sogge, Christopher D.; Zelditch, Steve 3 2017 Localized \(L^p\)-estimates for eigenfunctions. II. Zbl 1390.58019Sogge, Christopher D. 1 2017 Focal points and sup-norms of eigenfunctions. Zbl 1361.32011Sogge, Christopher D.; Zelditch, Steve 13 2016 Localized \(L^{p}\)-estimates of eigenfunctions: a note on an article of Hezari and Rivière. Zbl 1331.58036Sogge, Christopher D. 11 2016 Focal points and sup-norms of eigenfunctions II: the two-dimensional case. Zbl 1376.32011Sogge, Christopher D.; Zelditch, Steve 5 2016 Lower bounds for interior nodal sets of Steklov eigenfunctions. Zbl 1359.35116Sogge, Christopher D.; Wang, Xing; Zhu, Jiuyi 5 2016 A note on \(L^p\)-norms of quasi-modes. Zbl 1364.35219Sogge, Christopher D.; Zelditch, Steve 4 2016 Bilinear Kakeya-Nikodym averages of eigenfunctions on compact Riemannian surfaces. Zbl 1364.58016Miao, Changxing; Sogge, Christopher D.; Xi, Yakun; Yang, Jianwei 1 2016 On \(L^p\)-resolvent estimates and the density of eigenvalues for compact Riemannian manifolds. Zbl 1396.58025Bourgain, Jean; Shao, Peng; Sogge, Christopher D.; Yao, Xiaohua 16 2015 On integrals of eigenfunctions over geodesics. Zbl 1321.58023Chen, Xuehua; Sogge, Christopher D. 10 2015 On Kakeya-Nikodym averages, \(L^p\)-norms and lower bounds for nodal sets of eigenfunctions in higher dimensions. Zbl 1330.58023Blair, Matthew D.; Sogge, Christopher D. 9 2015 Refined and microlocal Kakeya-Nikodym bounds for eigenfunctions in two dimensions. Zbl 1321.58029Blair, Matthew D.; Sogge, Christopher D. 8 2015 Hangzhou lectures on eigenfunctions of the Laplacian. Zbl 1312.58001Sogge, Christopher D. 39 2014 The Strauss conjecture on Kerr black hole backgrounds. Zbl 1295.35327Lindblad, Hans; Metcalfe, Jason; Sogge, Christopher D.; Tohaneanu, Mihai; Wang, Chengbo 27 2014 On eigenfunction restriction estimates and \(L^4\)-bounds for compact surfaces with nonpositive curvature. Zbl 1307.58013Sogge, Christopher D.; Zelditch, Steve 15 2014 A few endpoint geodesic restriction estimates for eigenfunctions. Zbl 1293.58011Chen, Xuehua; Sogge, Christopher D. 13 2014 Concerning \(L^p\) resolvent estimates for simply connected manifolds of constant curvature. Zbl 1303.53052Huang, Shanlin; Sogge, Christopher D. 8 2014 Remarks on global solutions for nonlinear wave equations under the standard null conditions. Zbl 1262.35170Lindblad, Hans; Nakamura, Makoto; Sogge, Christopher D. 8 2013 Strichartz estimates for Dirichlet-wave equations in two dimensions with applications. Zbl 1246.35052Smith, Hart F.; Sogge, Christopher D.; Wang, Chengbo 22 2012 A natural lower bound for the size of nodal sets. Zbl 1329.35224Hezari, Hamid; Sogge, Christopher D. 19 2012 Lower bounds on the Hausdorff measure of nodal sets. II. Zbl 1283.58020Sogge, Christopher D.; Zelditch, Steve 17 2012 Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary. Zbl 1262.58015Blair, Matthew D.; Smith, Hart F.; Sogge, Chris D. 17 2012 Concerning the \(L^4\) norms of typical eigenfunctions on compact surfaces. Zbl 1317.58035Sogge, Christopher D.; Zelditch, Steve 7 2012 Lower bounds on the Hausdorff measure of nodal sets. Zbl 1242.58017Sogge, Christopher D.; Zelditch, Steve 28 2011 Kakeya-Nikodym averages and \(L^p\)-norms of eigenfunctions. Zbl 1234.35156Sogge, Christopher D. 23 2011 About the blowup of quasimodes on Riemannian manifolds. Zbl 1214.58012Sogge, Christopher D.; Toth, John A.; Zelditch, Steve 22 2011 On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles. Zbl 1193.35100Hidano, Kunio; Metcalfe, Jason; Smith, Hart F.; Sogge, Christopher D.; Zhou, Yi 35 2010 Concerning the wave equation on asymptotically Euclidean manifolds. Zbl 1231.35030Sogge, Christopher D.; Wang, Chengbo 21 2010 Global existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. Zbl 1213.35314Metcalfe, Jason; Sogge, Christopher D. 9 2010 Strichartz estimates for the wave equation on manifolds with boundary. Zbl 1198.58012Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 40 2009 Lectures on nonlinear wave equations. 2nd ed. Zbl 1165.35001Sogge, Christopher D. 51 2008 On Strichartz estimates for Schrödinger operators in compact manifolds with boundary. Zbl 1169.35012Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 23 2008 Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions. Zbl 1209.35083Du, Yi; Metcalfe, Jason; Sogge, Christopher D.; Zhou, Yi 21 2008 Fourier integrals in classical analysis. Paperback reprint of the hardback edition 1993. Zbl 1143.35002Sogge, Christopher D. 4 2008 On multilinear spectral cluster estimates for manifolds with boundary. Zbl 1146.58019Blair, Matthew D.; Smith, Hart F.; Sogge, Christopher D. 3 2008 On the \(L^p\) norm of spectral clusters for compact manifolds with boundary. Zbl 1189.58017Smith, Hart F.; Sogge, Christopher D. 37 2007 Global existence of null-form wave equations in exterior domains. Zbl 1138.35065Metcalfe, Jason; Sogge, Christopher D. 30 2007 Long-time existence of quasilinear wave equations exterior to star-shaped obstacles via energy methods. Zbl 1162.35052Metcalfe, Jason; Sogge, Christopher D. 44 2006 Global existence for Dirichlet-wave equations with quadratic nonlinearities in high dimensions. Zbl 1185.35140Metcalfe, Jason; Sogge, Christopher D. 13 2006 Hyperbolic trapped rays and global existence of quasilinear wave equations. Zbl 1077.35083Metcalfe, Jason; Sogge, Christopher D. 25 2005 Nonlinear hyperbolic equations in infinite homogeneous waveguides. Zbl 1078.35076Metcalfe, Jason; Sogge, Christopher D.; Stewart, Ann Ann 13 2005 Global existence of quasilinear, nonrelativistic wave equations satisfying the null condition. Zbl 1098.35112Metcalfe, Jason; Nakamura, Makoto; Sogge, Christopher D. 12 2005 Global existence of solutions to multiple speed systems of quasilinear wave equations in exterior domains. Zbl 1149.35055Metcalfe, Jason; Nakamura, Makoto; Sogge, Christopher D. 12 2005 Almost global existence for quasilinear wave equations in three space dimensions. Zbl 1055.35075Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 51 2004 Global existence for nonlinear wave equations with multiple speeds. Zbl 1052.35133Sogge, Christopher D. 16 2003 Almost global existence for some semilinear wave equations. Zbl 1031.35107Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 53 2002 Riemannian manifolds with maximal eigenfunction growth. Zbl 1018.58010Sogge, Christopher D.; Zelditch, Steve 43 2002 Global existence for a quasilinear wave equation outside of star-shaped domains. Zbl 1001.35087Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 27 2002 Eigenfunction and Bochner Riesz estimates on manifolds with boundary. Zbl 1017.58016Sogge, Christopher D. 18 2002 Global Strichartz estimates for nontrapping perturbations of the Laplacian. Zbl 0972.35014Smith, Hart F.; Sogge, Christopher D. 88 2000 On global existence for nonlinear wave equations outside of convex obstacles. Zbl 0957.35088Keel, Markus; Smith, Hart F.; Sogge, Christopher D. 5 2000 Null form estimates for \((1/2,1/2)\) symbols and local existence for a quasilinear Dirichlet-wave equation. Zbl 1016.35008Smith, Hart F.; Sogge, Christopher D. 1 2000 Concerning Nikodym-type sets in 3-dimensional curved spaces. Zbl 0968.42016Sogge, Christopher D. 9 1999 Averages over curves with torsion. Zbl 0934.42008Oberlin, Daniel; Smith, Hart F.; Sogge, Christopher D. 4 1998 Weighted Strichartz estimates and global existence for semilinear wave equations. Zbl 0893.35075Georgiev, Vladimir; Lindblad, Hans; Sogge, Christopher D. 122 1997 Local smoothing estimates related to the circular maximal theorem. Zbl 0877.42006Schlag, Wilhelm; Sogge, Christopher D. 20 1997 Negative results for Nikodym maximal functions and related oscillatory integrals in curved space. Zbl 0884.42016Minicozzi, William P. II; Sogge, Christopher D. 14 1997 Long-time existence for small amplitude semilinear wave equations. Zbl 0869.35064Lindblad, Hans; Sogge, Christopher D. 68 1996 Restriction theorems and semilinear Klein-Gordon equations in \((1+3)\)-dimensions. Zbl 0865.35077Lindblad, Hans; Sogge, Christopher D. 6 1996 On existence and scattering with minimal regularity for semilinear wave equations. Zbl 0846.35085Lindblad, Hans; Sogge, Christopher D. 165 1995 Lectures on nonlinear wave equations. Zbl 1089.35500Sogge, Christopher D. 82 1995 On the critical semilinear wave equation outside convex obstacles. Zbl 0860.35081Smith, Hart F.; Sogge, Christopher D. 35 1995 Maximal operators associated to hypersurfaces with one nonvanishing principal curvature. Zbl 0880.42011Sogge, Christopher D. 12 1995 Smoothing estimates for the wave equation and applications. Zbl 0901.35050Sogge, Christopher D. 2 1995 On Strichartz and eigenfunction estimates for low regularity metrics. Zbl 0832.35018Smith, Hart F.; Sogge, Christopher D. 12 1994 \(L^ p\) regularity for the wave equation with strictly convex obstacles. Zbl 0805.35169Smith, Hart F.; Sogge, Christopher D. 6 1994 Fourier integrals in classical analysis. Zbl 0783.35001Sogge, Christopher D. 198 1993 Local smoothing of Fourier integral operators and Carleson-Sjölin estimates. Zbl 0776.58037Mockenhaupt, Gerd; Seeger, Andreas; Sogge, Christopher D. 73 1993 On local existence for nonlinear wave equations satisfying variable coefficient null conditions. Zbl 0792.35125Sogge, Christopher D. 3 1993 \(L^ p\) estimates for the wave equation and applications. Zbl 0796.35111Sogge, Christopher D. 2 1993 Wave front sets, local smoothing and Bourgain’s circular maximal theorem. Zbl 0759.42016Mockenhaupt, Gerd; Seeger, Andreas; Sogge, Christopher D. 52 1992 Uniqueness in Cauchy problems for hyperbolic differential operators. Zbl 0763.35012Sogge, Christopher D. 6 1992 Sobolev estimates for the wave operator on compact manifolds. Zbl 0799.35157Jerison, D.; Sogge, C. D.; Zhou, Z. 1 1992 Decay estimates for Schrödinger operators. Zbl 0743.35008Journé, J.-L.; Soffer, A.; Sogge, C. D. 114 1991 Regularity properties of Fourier integral operators. Zbl 0754.58037Seeger, Andreas; Sogge, Christopher D.; Stein, Elias M. 85 1991 Propagation of singularities and maximal functions in the plane. Zbl 0754.35004Sogge, Christopher D. 39 1991 Strong uniqueness theorems for second order elliptic differential equations. Zbl 0734.35012Sogge, Christopher D. 29 1990 A unique continuation theorem for second order parabolic differential operators. Zbl 0704.35016Sogge, C. D. 19 1990 Averages over hypersurfaces. Smoothness of generalized Radon transforms. Zbl 0695.42012Sogge, C. D.; Stein, Elias M. 17 1990 Oscillatory integrals associated to folding canonical relations. Zbl 0746.58076Pan, Yibiao; Sogge, Christopher D. 14 1990 \(L^ p \to{} L^{p'}\) estimates for time-dependent Schrödinger operators. Zbl 0751.35011Journé, J. L.; Soffer, A.; Sogge, C. D. 3 1990 On the boundedness of functions of (pseudo-) differential operators on compact manifolds. Zbl 0698.35169Seeger, A.; Sogge, C. D. 40 1989 Bounds for eigenfunctions of differential operators. Zbl 0703.35133Seeger, A.; Sogge, C. D. 28 1989 Oscillatory integrals and unique continuation for second order elliptic differential equations. Zbl 0703.35027Sogge, Christopher D. 13 1989 Remarks on \(L^ 2\) restriction theorems for Riemannian manifolds. Zbl 0681.42009Sogge, C. D. 2 1989 Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds. Zbl 0641.46011Sogge, Christopher D. 122 1988 ...and 11 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,232 Authors 60 Sogge, Christopher D. 27 Wang, Chengbo 24 Seeger, Andreas 21 Metcalfe, Jason L. 20 Lee, Sanghyuk 17 Kenig, Carlos Eduardo 17 Smith, Hart F. 16 Burq, Nicolas 16 Zhang, Junyong 16 Zhou, Yi 14 Cuccagna, Scipio 14 Hidano, Kunio 14 Iosevich, Alex 14 Schlag, Wilhelm 14 Tataru, Daniel 13 Goldberg, Michael Joseph 13 Lai, Ningan 13 Merle, Frank 13 Seo, Ihyeok 13 Tzvetkov, Nikolay 12 Blair, Matthew D. 12 D’Ancona, Piero 12 Green, William R. 12 Planchon, Fabrice 12 Ruzhansky, Michael V. 12 Soffer, Avraham 12 Toth, John Andrew 11 Fan, Dashan 11 Han, Wei 11 Müller, Detlef 11 Vega, Luis 11 Yao, Xiaohua 11 Zelditch, Steve 11 Zha, Dongbing 11 Zheng, Jiqiang 10 Fang, Daoyuan 10 Tao, Terence 10 Tohaneanu, Mihai 9 Duyckaerts, Thomas 9 Erdoğan, Mehmet Burak 9 Kubo, Hideo 9 Miao, Changxing 9 Palmieri, Alessandro 9 Wakasa, Kyouhei 9 Witt, Ingo 9 Yin, Huicheng 9 Zaag, Hatem 9 Zhu, Jiuyi 8 Cuenin, Jean-Claude 8 D’Abbicco, Marcello 8 Galkowski, Jeffrey 8 Hassell, Andrew 8 Ivanovici, Oana 8 Kharibegashvili, S. S. 8 Manna, Ramesh 8 Mizutani, Haruya 8 Sikora, Adam S. 8 Staubach, Wolfgang 8 Stein, Elias Menachem 8 Sugimoto, Mitsuru 8 Tacy, Melissa 8 Takamura, Hiroyuki 8 Yan, Lixin 7 Casarino, Valentina 7 Dodson, Benjamin G. 7 Donninger, Roland 7 Evéquoz, Gilles 7 Gerard, Patrick 7 Greenblatt, Michael 7 Jleli, Mohamed Boussairi 7 Katayama, Soichiro 7 Klainerman, Sergiu 7 Koch, Herbert 7 Lawrie, Andrew G. W. 7 Lebeau, Gilles 7 Lindblad, Hans 7 Marzuola, Jeremy L. 7 Oh, Tadahiro 7 Samet, Bessem 7 Xi, Yakun 6 Canzani, Yaiza 6 Chen, Jiecheng 6 Chen, Peng 6 Ciatti, Paolo 6 Dong, Shijie 6 Ebert, Marcelo Rempel 6 Frank, Rupert L. 6 Germain, Pierre 6 Han, Xiaolong 6 Hickman, Jonathan 6 Hong, Sunggeum 6 Kwon, Yehyun 6 Mandel, Rainer 6 Martini, Alessio 6 Nicola, Fabio 6 Ozawa, Tohru 6 Phong, Duong Hong 6 Pramanik, Malabika 6 Ratnakumar, P. K. 6 Taylor, Michael Eugene ...and 1,132 more Authors all top 5 Cited in 230 Serials 98 Journal of Functional Analysis 89 Journal of Differential Equations 80 Communications in Partial Differential Equations 70 Communications in Mathematical Physics 70 Journal of Mathematical Analysis and Applications 68 Transactions of the American Mathematical Society 47 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 46 Proceedings of the American Mathematical Society 43 Duke Mathematical Journal 39 Advances in Mathematics 34 The Journal of Geometric Analysis 32 Mathematische Annalen 32 The Journal of Fourier Analysis and Applications 21 Journal d’Analyse Mathématique 21 Mathematische Zeitschrift 20 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 20 Discrete and Continuous Dynamical Systems 19 Forum Mathematicum 18 Revista Matemática Iberoamericana 18 Journal de Mathématiques Pures et Appliquées. 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Mathematics 4 Bulletin of Mathematical Sciences 4 Forum of Mathematics, Sigma 4 Stochastic and Partial Differential Equations. Analysis and Computations 3 Applicable Analysis 3 Inverse Problems 3 Mathematics of Computation 3 Applied Mathematics and Computation 3 Functional Analysis and its Applications 3 Indiana University Mathematics Journal 3 Journal of the London Mathematical Society. Second Series 3 Journal für die Reine und Angewandte Mathematik 3 Manuscripta Mathematica 3 Quarterly of Applied Mathematics 3 Annals of Global Analysis and Geometry 3 Annales de l’Institut Henri Poincaré. Physique Théorique 3 Potential Analysis 3 NoDEA. Nonlinear Differential Equations and Applications 3 Nonlinear Analysis. Real World Applications 3 Journal of the Institute of Mathematics of Jussieu 3 Journal of Pseudo-Differential Operators and Applications 3 Journal of Spectral Theory 3 Séminaire Laurent Schwartz. EDP et Applications 2 Classical and Quantum Gravity 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Russian Mathematical Surveys 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 2 Applied Mathematics and Optimization 2 Archiv der Mathematik 2 Bulletin de la Société Mathématique de France 2 Geometriae Dedicata 2 Glasgow Mathematical Journal 2 Memoirs of the American Mathematical Society 2 Proceedings of the Japan Academy. Series A 2 Proceedings of the London Mathematical Society. Third Series ...and 130 more Serials all top 5 Cited in 52 Fields 1,144 Partial differential equations (35-XX) 360 Harmonic analysis on Euclidean spaces (42-XX) 241 Global analysis, analysis on manifolds (58-XX) 139 Operator theory (47-XX) 101 Quantum theory (81-XX) 61 Functional analysis (46-XX) 55 Differential geometry (53-XX) 48 Abstract harmonic analysis (43-XX) 46 Fluid mechanics (76-XX) 42 Number theory (11-XX) 41 Dynamical systems and ergodic theory (37-XX) 34 Relativity and gravitational theory (83-XX) 28 Integral transforms, operational calculus (44-XX) 28 Probability theory and stochastic processes (60-XX) 26 Topological groups, Lie groups (22-XX) 25 Special functions (33-XX) 24 Mechanics of deformable solids (74-XX) 21 Measure and integration (28-XX) 18 Numerical analysis (65-XX) 18 Optics, electromagnetic theory (78-XX) 17 Systems theory; control (93-XX) 14 Ordinary differential equations (34-XX) 12 Functions of a complex variable (30-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 11 Approximations and expansions (41-XX) 11 Statistical mechanics, structure of matter (82-XX) 10 Real functions (26-XX) 9 Several complex variables and analytic spaces (32-XX) 7 Potential theory (31-XX) 7 Integral equations (45-XX) 7 Mechanics of particles and systems (70-XX) 5 General and overarching topics; collections (00-XX) 5 Combinatorics (05-XX) 5 Algebraic geometry (14-XX) 5 Computer science (68-XX) 4 Difference and functional equations (39-XX) 4 Convex and discrete geometry (52-XX) 4 Information and communication theory, circuits (94-XX) 3 Geometry (51-XX) 3 Statistics (62-XX) 3 Astronomy and astrophysics (85-XX) 3 Geophysics (86-XX) 3 Operations research, mathematical programming (90-XX) 2 History and biography (01-XX) 2 Biology and other natural sciences (92-XX) 1 Mathematical logic and foundations (03-XX) 1 Field theory and polynomials (12-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Group theory and generalizations (20-XX) 1 Sequences, series, summability (40-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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