Edit Profile (opens in new tab) Warren, Micah W. Co-Author Distance Author ID: warren.micah-w Published as: Warren, Micah; Warren, Micah W. External Links: MGP · ORCID Documents Indexed: 33 Publications since 2008, including 1 Book and 2 Additional arXiv Preprints Co-Authors: 13 Co-Authors with 24 Joint Publications 240 Co-Co-Authors all top 5 Co-Authors 9 single-authored 5 Chen, Jingyi 5 Yuan, Yu 4 Bhattacharya, Arunima 4 Streets, Jeffrey D. 3 Ache, Antonio G. 2 Gursky, Matthew J. 2 Kim, Young-Heon 2 McCann, Robert J. 1 Brendle, Simon 1 Drugan, Gregory 1 He, Weiyong 1 Kitagawa, Jun 1 Pass, Brendan W. all top 5 Serials 3 Advances in Mathematics 2 Communications on Pure and Applied Mathematics 2 Proceedings of the American Mathematical Society 2 IMRN. International Mathematics Research Notices 2 Communications in Partial Differential Equations 2 Communications in Analysis and Geometry 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Canadian Journal of Mathematics 1 Journal of Differential Equations 1 Journal of Differential Geometry 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematische Zeitschrift 1 Pacific Journal of Mathematics 1 Results in Mathematics 1 Transactions of the American Mathematical Society 1 Differential Geometry and its Applications 1 SIAM Journal on Mathematical Analysis 1 Calculus of Variations and Partial Differential Equations 1 Mathematical Research Letters 1 Advances in Geometry 1 Communications on Pure and Applied Analysis 1 De Gruyter Graduate all top 5 Fields 22 Partial differential equations (35-XX) 16 Differential geometry (53-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 5 Global analysis, analysis on manifolds (58-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Potential theory (31-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Operator theory (47-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Operations research, mathematical programming (90-XX) 1 Systems theory; control (93-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 29 Publications have been cited 248 times in 156 Documents Cited by ▼ Year ▼ Hessian estimates for the sigma-2 equation in dimension 3. Zbl 1173.35388 Warren, Micah; Yuan, Yu 33 2009 Calibrations associated to Monge-Ampère equations. Zbl 1209.53041 Warren, Micah 22 2010 Hessian and gradient estimates for three dimensional special Lagrangian equations with large phase. Zbl 1221.35081 Warren, Micah; Yuan, Yu 21 2010 Pseudo-Riemann geometry calibrates optimal transportation. Zbl 1222.49059 Kim, Young-Heon; McCann, Robert J.; Warren, Micah 20 2010 A priori estimate for convex solutions to special Lagrangian equations and its application. Zbl 1171.35340 Chen, Jingyi; Yuan, Yu; Warren, Micah 18 2009 A boundary value problem for minimal Lagrangian graphs. Zbl 1195.53081 Brendle, Simon; Warren, Micah 16 2010 Nonpolynomial entire solutions to \(\sigma_k\) equations. Zbl 1347.35112 Warren, Micah 15 2016 Existence of complete conformal metrics of negative Ricci curvature on manifolds with boundary. Zbl 1214.53035 Gursky, Matthew; Streets, Jeffrey; Warren, Micah 14 2011 Explicit gradient estimates for minimal Lagrangian surfaces of dimension two. Zbl 1181.53042 Warren, Micah; Yuan, Yu 10 2009 On the regularity of Hamiltonian stationary Lagrangian submanifolds. Zbl 1417.35017 Chen, Jingyi; Warren, Micah 10 2019 Rectifiability of optimal transportation plans. Zbl 1248.49060 McCann, Robert J.; Pass, Brendan; Warren, Micah 9 2012 Evans-Krylov estimates for a nonconvex Monge-Ampère equation. Zbl 1342.35124 Streets, Jeffrey; Warren, Micah 9 2016 A Liouville type theorem for special Lagrangian equations with constraints. Zbl 1146.35039 Warren, Micah; Yuan, Yu 8 2008 Regularity for the optimal transportation problem with Euclidean distance squared cost on the embedded sphere. Zbl 1273.35275 Kitagawa, Jun; Warren, Micah 5 2012 Parabolic optimal transport equations on manifolds. Zbl 1253.49036 Kim, Young-Heon; Streets, Jeffrey; Warren, Micah 5 2012 A Liouville property for gradient graphs and a Bernstein problem for Hamiltonian stationary equations. Zbl 1339.35115 Warren, Micah W. 5 2016 Coarse Ricci curvature as a function on \({M\times M}\). Zbl 1385.53030 Ache, Antonio G.; Warren, Micah W. 4 2017 Regularity bootstrapping for 4th-order nonlinear elliptic equations. Zbl 1470.35090 Bhattacharya, Arunima; Warren, Micah 4 2021 Ricci curvature and the manifold learning problem. Zbl 1415.93297 Ache, Antonio G.; Warren, Micah W. 4 2019 Legendrian curve shortening flow in \(\mathbb{R}^3\). Zbl 1397.53080 Drugan, Gregory; He, Weiyong; Warren, Micah W. 3 2018 Regularity for a log-concave to log-concave mass transfer problem with near Euclidean cost. Zbl 1239.49063 Warren, Micah 2 2011 A Bernstein result and counterexample for entire solutions to Donaldson’s equation. Zbl 1338.35174 Warren, Micah 2 2016 \(C^{2,\alpha}\) estimates for solutions to almost linear elliptic equations. Zbl 1471.35134 Bhattacharya, Arunima; Warren, Micah 2 2021 Radial solutions of a fourth order Hamiltonian stationary equation. Zbl 1524.70052 Chen, Jingyi; Warren, Micah 2 2018 A McLean theorem for the moduli space of Lie solutions to mass transport equations. Zbl 1226.49043 Warren, Micah 1 2011 On solutions to Cournot-Nash equilibria equations on the sphere. Zbl 1378.49054 Warren, Micah 1 2014 Approximating coarse Ricci curvature on submanifolds of Euclidean space. Zbl 1492.53056 Ache, Antonio G.; Warren, Micah W. 1 2022 Regularity of Hamiltonian stationary equations in symplectic manifolds. Zbl 1515.53079 Bhattacharya, Arunima; Chen, Jingyi; Warren, Micah 1 2023 Interior Schauder estimates for the fourth order Hamiltonian stationary equation in two dimensions. Zbl 1426.35113 Bhattacharya, Arunima; Warren, Micah 1 2019 Regularity of Hamiltonian stationary equations in symplectic manifolds. Zbl 1515.53079 Bhattacharya, Arunima; Chen, Jingyi; Warren, Micah 1 2023 Approximating coarse Ricci curvature on submanifolds of Euclidean space. Zbl 1492.53056 Ache, Antonio G.; Warren, Micah W. 1 2022 Regularity bootstrapping for 4th-order nonlinear elliptic equations. Zbl 1470.35090 Bhattacharya, Arunima; Warren, Micah 4 2021 \(C^{2,\alpha}\) estimates for solutions to almost linear elliptic equations. Zbl 1471.35134 Bhattacharya, Arunima; Warren, Micah 2 2021 On the regularity of Hamiltonian stationary Lagrangian submanifolds. Zbl 1417.35017 Chen, Jingyi; Warren, Micah 10 2019 Ricci curvature and the manifold learning problem. Zbl 1415.93297 Ache, Antonio G.; Warren, Micah W. 4 2019 Interior Schauder estimates for the fourth order Hamiltonian stationary equation in two dimensions. Zbl 1426.35113 Bhattacharya, Arunima; Warren, Micah 1 2019 Legendrian curve shortening flow in \(\mathbb{R}^3\). Zbl 1397.53080 Drugan, Gregory; He, Weiyong; Warren, Micah W. 3 2018 Radial solutions of a fourth order Hamiltonian stationary equation. Zbl 1524.70052 Chen, Jingyi; Warren, Micah 2 2018 Coarse Ricci curvature as a function on \({M\times M}\). Zbl 1385.53030 Ache, Antonio G.; Warren, Micah W. 4 2017 Nonpolynomial entire solutions to \(\sigma_k\) equations. Zbl 1347.35112 Warren, Micah 15 2016 Evans-Krylov estimates for a nonconvex Monge-Ampère equation. Zbl 1342.35124 Streets, Jeffrey; Warren, Micah 9 2016 A Liouville property for gradient graphs and a Bernstein problem for Hamiltonian stationary equations. Zbl 1339.35115 Warren, Micah W. 5 2016 A Bernstein result and counterexample for entire solutions to Donaldson’s equation. Zbl 1338.35174 Warren, Micah 2 2016 On solutions to Cournot-Nash equilibria equations on the sphere. Zbl 1378.49054 Warren, Micah 1 2014 Rectifiability of optimal transportation plans. Zbl 1248.49060 McCann, Robert J.; Pass, Brendan; Warren, Micah 9 2012 Regularity for the optimal transportation problem with Euclidean distance squared cost on the embedded sphere. Zbl 1273.35275 Kitagawa, Jun; Warren, Micah 5 2012 Parabolic optimal transport equations on manifolds. Zbl 1253.49036 Kim, Young-Heon; Streets, Jeffrey; Warren, Micah 5 2012 Existence of complete conformal metrics of negative Ricci curvature on manifolds with boundary. Zbl 1214.53035 Gursky, Matthew; Streets, Jeffrey; Warren, Micah 14 2011 Regularity for a log-concave to log-concave mass transfer problem with near Euclidean cost. Zbl 1239.49063 Warren, Micah 2 2011 A McLean theorem for the moduli space of Lie solutions to mass transport equations. Zbl 1226.49043 Warren, Micah 1 2011 Calibrations associated to Monge-Ampère equations. Zbl 1209.53041 Warren, Micah 22 2010 Hessian and gradient estimates for three dimensional special Lagrangian equations with large phase. Zbl 1221.35081 Warren, Micah; Yuan, Yu 21 2010 Pseudo-Riemann geometry calibrates optimal transportation. Zbl 1222.49059 Kim, Young-Heon; McCann, Robert J.; Warren, Micah 20 2010 A boundary value problem for minimal Lagrangian graphs. Zbl 1195.53081 Brendle, Simon; Warren, Micah 16 2010 Hessian estimates for the sigma-2 equation in dimension 3. Zbl 1173.35388 Warren, Micah; Yuan, Yu 33 2009 A priori estimate for convex solutions to special Lagrangian equations and its application. Zbl 1171.35340 Chen, Jingyi; Yuan, Yu; Warren, Micah 18 2009 Explicit gradient estimates for minimal Lagrangian surfaces of dimension two. Zbl 1181.53042 Warren, Micah; Yuan, Yu 10 2009 A Liouville type theorem for special Lagrangian equations with constraints. Zbl 1146.35039 Warren, Micah; Yuan, Yu 8 2008 all cited Publications top 5 cited Publications all top 5 Cited by 167 Authors 16 Warren, Micah W. 10 Bao, Jiguang 10 Yuan, Yu 8 Chen, Jingyi 7 Bhattacharya, Arunima 7 Huang, Rongli 7 Liu, Zixiao 4 McCann, Robert J. 4 Shen, Weiming 3 Ache, Antonio G. 3 Collins, Tristan Clifford 3 Han, Qing 3 Harvey, Reese 3 Khan, Gabriel J. H. 3 Lawson, Herbert Blaine jun. 3 Li, Haigang 3 Li, Zhisu 3 Nguyen, Luc 3 Shankar, Ravi 3 Streets, Jeffrey D. 3 Zhang, Jun 2 Abedin, Farhan 2 Carlier, Guillaume 2 Chen, ChuanQiang 2 Chu, Jianchun 2 Dai, Guowei 2 Duncan, Jonah A. J. 2 Figalli, Alessio 2 Froese Hamfeldt, Brittany 2 Godoy, Yamile 2 González, María del Mar 2 Gursky, Matthew J. 2 Han, Yingbo 2 Kitagawa, Jun 2 Lesniewski, Jacob 2 Li, Caiyan 2 Li, Dongsheng 2 Li, YanYan 2 Ou, Qianzhong 2 Pan, Shujing 2 Picard, Sebastien 2 Rossi, Federico Alberto 2 Salvai, Marcos 2 Wang, Jun 2 Wang, Yue 2 Weinkove, Ben 2 Xiang, Ni 2 Yau, Shing-Tung 2 Ye, Yunhua 2 Zhou, Xingchen 1 Ahmad, Najma 1 Akgüller, Ömer 1 An, Ning 1 Angella, Daniele 1 Bauer, Frank 1 Berman, Robert J. 1 Bonafini, Mauro 1 Caboussat, Alexandre 1 Caffarelli, Luis Ángel 1 Chang, Shu-Cheng 1 Chau, Albert 1 Chen, Juanjuan 1 Chen, Li 1 Chen, Shibing 1 Conti, Diego 1 Dai, Limei 1 Dai, Song 1 De Philippis, Guido 1 Ding, Qi 1 Dong, Weisong 1 D’Onofrio, Roberto 1 Du, Shi-Zhong 1 Duan, Shuangshuang 1 Fioresi, Rita 1 Fox, Daniel J. F. 1 Goffi, Alessandro 1 Graham, C. Robin 1 Grementieri, Luca 1 Guan, Pengfei 1 Gukov, Sergei 1 Han, Xiaoli 1 He, Chunlei 1 He, Yan 1 Hong, Jin 1 Hua, Bobo 1 Huang, Liding 1 Huang, Shoujun 1 Huang, Yong 1 Jacob, Adam 1 Jiang, Tangyu 1 Jin, Xishen 1 Jost, Jürgen 1 Ketterer, Christian 1 Kim, Hwa Kil 1 Kim, Young-Heon 1 Korman, Jonathan 1 Krioukov, Dmitri 1 Krylov, Nicolaĭ Vladimirovich 1 Lee, Hojoo 1 Léger, Flavien ...and 67 more Authors all top 5 Cited in 61 Serials 19 Calculus of Variations and Partial Differential Equations 8 Proceedings of the American Mathematical Society 7 Advances in Mathematics 7 Journal of Differential Equations 7 Journal of Functional Analysis 7 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 6 The Journal of Geometric Analysis 5 Journal of Mathematical Analysis and Applications 5 Transactions of the American Mathematical Society 4 Mathematische Annalen 3 Communications on Pure and Applied Mathematics 3 Discrete and Continuous Dynamical Systems 3 Communications on Pure and Applied Analysis 2 Archive for Rational Mechanics and Analysis 2 Israel Journal of Mathematics 2 Journal of Geometry and Physics 2 Archiv der Mathematik 2 Duke Mathematical Journal 2 Mathematische Zeitschrift 2 Numerische Mathematik 2 Pacific Journal of Mathematics 2 Annals of Global Analysis and Geometry 2 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2 International Journal of Mathematics 2 Differential Geometry and its Applications 2 Communications in Partial Differential Equations 2 Communications in Contemporary Mathematics 2 Analysis & PDE 2 Communications in Mathematics and Statistics 2 Information Geometry 2 Pure and Applied Analysis 1 Communications in Mathematical Physics 1 Annales de l’Institut Fourier 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Annales Polonici Mathematici 1 Indiana University Mathematics Journal 1 Journal für die Reine und Angewandte Mathematik 1 Proceedings of the London Mathematical Society. Third Series 1 Results in Mathematics 1 Chinese Annals of Mathematics. Series B 1 Discrete & Computational Geometry 1 Applied Mathematics Letters 1 Journal of Scientific Computing 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 SIAM Journal on Mathematical Analysis 1 Bulletin of the American Mathematical Society. New Series 1 SIAM Journal on Optimization 1 Applied Mathematics. Series B (English Edition) 1 Soft Computing 1 Discrete Dynamics in Nature and Society 1 Journal of Mathematical Study 1 Annals of Mathematics. Second Series 1 Journal of the European Mathematical Society (JEMS) 1 Acta Mathematica Sinica. English Series 1 Advances in Geometry 1 Advanced Nonlinear Studies 1 Journal of Fixed Point Theory and Applications 1 SIAM Journal on Imaging Sciences 1 Bulletin of Mathematical Sciences 1 SIAM/ASA Journal on Uncertainty Quantification 1 Peking Mathematical Journal all top 5 Cited in 27 Fields 109 Partial differential equations (35-XX) 65 Differential geometry (53-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 15 Global analysis, analysis on manifolds (58-XX) 10 Several complex variables and analytic spaces (32-XX) 8 Operations research, mathematical programming (90-XX) 6 Numerical analysis (65-XX) 3 Algebraic geometry (14-XX) 3 Probability theory and stochastic processes (60-XX) 3 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Systems theory; control (93-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Convex and discrete geometry (52-XX) 2 Manifolds and cell complexes (57-XX) 2 Statistics (62-XX) 2 Computer science (68-XX) 2 Information and communication theory, circuits (94-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Ordinary differential equations (34-XX) 1 Approximations and expansions (41-XX) 1 Operator theory (47-XX) 1 Mechanics of particles and systems (70-XX) 1 Fluid mechanics (76-XX) 1 Quantum theory (81-XX) Citations by Year