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Author ID: knopf.dan Recent zbMATH articles by "Knopf, Dan"
Published as: Knopf, Dan
Documents Indexed: 38 Publications since 2000, including 6 Books and 2 Additional arXiv Preprints
Co-Authors: 26 Co-Authors with 32 Joint Publications
537 Co-Co-Authors

Publications by Year

Citations contained in zbMATH Open

31 Publications have been cited 978 times in 702 Documents Cited by Year
The Ricci flow: an introduction. Zbl 1086.53085
Chow, Bennett; Knopf, Dan
261
2004
The Ricci flow: techniques and applications. Part I: Geometric aspects. Zbl 1157.53034
Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei
197
2007
Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons. Zbl 1069.53036
Feldman, Mikhail; Ilmanen, Tom; Knopf, Dan
101
2003
The Ricci flow: techniques and applications. Part II: Analytic aspects. Zbl 1157.53035
Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei
73
2008
The Ricci flow: techniques and applications. Part III: Geometric-analytic aspects. Zbl 1216.53057
Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei
64
2010
Stability of the Ricci flow at Ricci-flat metrics. Zbl 1028.53043
Guenther, Christine; Isenberg, James; Knopf, Dan
32
2002
An example of neckpinching for Ricci flow on \(S^{n+1}\). Zbl 1064.58022
Angenent, Sigurd; Knopf, Dan
31
2004
Precise asymptotics of the Ricci flow neckpinch. Zbl 1145.53049
Angenent, Sigurd B.; Knopf, Dan
22
2007
Universality in mean curvature flow neckpinches. Zbl 1329.53093
Gang, Zhou; Knopf, Dan
17
2015
Quasi-convergence of model geometries under the Ricci flow. Zbl 1020.53044
Knopf, Dan; McLeod, Kevin
16
2001
Degenerate neckpinches in Ricci flow. Zbl 1329.53102
Angenent, Sigurd B.; Isenberg, James; Knopf, Dan
16
2015
Local monotonicity and mean value formulas for evolving Riemannian manifolds. Zbl 1170.35050
Ecker, Klaus; Knopf, Dan; Ni, Lei; Topping, Peter
14
2008
The Ricci flow: techniques and applications. Part IV: Long-time solutions and related topics. Zbl 1341.53001
Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei
14
2015
A lower bound for the diameter of solutions to the Ricci flow with nonzero \(H^1(M^n, \mathbb R)\). Zbl 1048.58022
Ilmanen, Tom; Knopf, Dan
12
2003
Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow. Zbl 1440.53106
Gang, Zhou; Knopf, Dan; Sigal, Israel Michael
12
2018
Estimating the trace-free Ricci tensor in Ricci flow. Zbl 1172.53043
Knopf, Dan
10
2009
Formal matched asymptotics for degenerate Ricci flow neckpinches. Zbl 1225.53061
Angenent, Sigurd B.; Isenberg, James; Knopf, Dan
10
2011
New Li-Yau-Hamilton inequalities for the Ricci flow via the space-time approach. Zbl 1048.53026
Chow, Bennett; Knopf, Dan
9
2002
Asymptotic stability of the cross curvature flow at a hyperbolic metric. Zbl 1168.53034
Knopf, Dan; Young, Andrea
7
2009
Ricci flow neckpinches without rotational symmetry. Zbl 1357.53078
Isenberg, James; Knopf, Dan; Šešum, Nataša
7
2016
Quasi-convergence of the Ricci flow. Zbl 1027.53075
Knopf, Dan
6
2000
Positivity of Ricci curvature under the Kähler-Ricci flow. Zbl 1118.53045
Knopf, Dan
6
2006
Non-Kähler Ricci flow singularities modeled on Kähler-Ricci solitons. Zbl 1431.53103
Isenberg, James; Knopf, Dan; Šešum, Nataša
6
2019
Minimally invasive surgery for Ricci flow singularities. Zbl 1258.53066
Angenent, Sigurd B.; Caputo, M. Cristina; Knopf, Dan
6
2012
Convergence and stability of locally \(\mathbb R^N\)-invariant solutions of Ricci flow. Zbl 1176.53068
Knopf, Dan
6
2009
Dynamic instability of \(\mathbb {CP}^N\) under Ricci flow. Zbl 1408.53090
Knopf, Dan; Šešum, Nataša
5
2019
Linear stability of homogeneous Ricci solutions. Zbl 1126.53040
Guenther, Christine; Isenberg, James; Knopf, Dan
5
2006
Ricci solitons, conical singularities, and nonuniqueness. Zbl 1503.53091
Angenent, Sigurd B.; Knopf, Dan
4
2022
Cross curvature flow on a negatively curved solid torus. Zbl 1211.53083
DeBlois, Jason; Knopf, Dan; Young, Andrea
4
2010
Sphere bundles with \(1/4\)-pinched fiberwise metrics. Zbl 1369.57032
Farrell, Thomas; Gang, Zhou; Knopf, Dan; Ontaneda, Pedro
3
2017
Hamilton’s injectivity radius estimate for sequences with almost nonnegative curvature operators. Zbl 1041.53042
Chow, Bennett; Knopf, Dan; Lu, Peng
2
2002
Ricci solitons, conical singularities, and nonuniqueness. Zbl 1503.53091
Angenent, Sigurd B.; Knopf, Dan
4
2022
Non-Kähler Ricci flow singularities modeled on Kähler-Ricci solitons. Zbl 1431.53103
Isenberg, James; Knopf, Dan; Šešum, Nataša
6
2019
Dynamic instability of \(\mathbb {CP}^N\) under Ricci flow. Zbl 1408.53090
Knopf, Dan; Šešum, Nataša
5
2019
Neckpinch dynamics for asymmetric surfaces evolving by mean curvature flow. Zbl 1440.53106
Gang, Zhou; Knopf, Dan; Sigal, Israel Michael
12
2018
Sphere bundles with \(1/4\)-pinched fiberwise metrics. Zbl 1369.57032
Farrell, Thomas; Gang, Zhou; Knopf, Dan; Ontaneda, Pedro
3
2017
Ricci flow neckpinches without rotational symmetry. Zbl 1357.53078
Isenberg, James; Knopf, Dan; Šešum, Nataša
7
2016
Universality in mean curvature flow neckpinches. Zbl 1329.53093
Gang, Zhou; Knopf, Dan
17
2015
Degenerate neckpinches in Ricci flow. Zbl 1329.53102
Angenent, Sigurd B.; Isenberg, James; Knopf, Dan
16
2015
The Ricci flow: techniques and applications. Part IV: Long-time solutions and related topics. Zbl 1341.53001
Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei
14
2015
Minimally invasive surgery for Ricci flow singularities. Zbl 1258.53066
Angenent, Sigurd B.; Caputo, M. Cristina; Knopf, Dan
6
2012
Formal matched asymptotics for degenerate Ricci flow neckpinches. Zbl 1225.53061
Angenent, Sigurd B.; Isenberg, James; Knopf, Dan
10
2011
The Ricci flow: techniques and applications. Part III: Geometric-analytic aspects. Zbl 1216.53057
Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei
64
2010
Cross curvature flow on a negatively curved solid torus. Zbl 1211.53083
DeBlois, Jason; Knopf, Dan; Young, Andrea
4
2010
Estimating the trace-free Ricci tensor in Ricci flow. Zbl 1172.53043
Knopf, Dan
10
2009
Asymptotic stability of the cross curvature flow at a hyperbolic metric. Zbl 1168.53034
Knopf, Dan; Young, Andrea
7
2009
Convergence and stability of locally \(\mathbb R^N\)-invariant solutions of Ricci flow. Zbl 1176.53068
Knopf, Dan
6
2009
The Ricci flow: techniques and applications. Part II: Analytic aspects. Zbl 1157.53035
Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei
73
2008
Local monotonicity and mean value formulas for evolving Riemannian manifolds. Zbl 1170.35050
Ecker, Klaus; Knopf, Dan; Ni, Lei; Topping, Peter
14
2008
The Ricci flow: techniques and applications. Part I: Geometric aspects. Zbl 1157.53034
Chow, Bennett; Chu, Sun-Chin; Glickenstein, David; Guenther, Christine; Isenberg, James; Ivey, Tom; Knopf, Dan; Lu, Peng; Luo, Feng; Ni, Lei
197
2007
Precise asymptotics of the Ricci flow neckpinch. Zbl 1145.53049
Angenent, Sigurd B.; Knopf, Dan
22
2007
Positivity of Ricci curvature under the Kähler-Ricci flow. Zbl 1118.53045
Knopf, Dan
6
2006
Linear stability of homogeneous Ricci solutions. Zbl 1126.53040
Guenther, Christine; Isenberg, James; Knopf, Dan
5
2006
The Ricci flow: an introduction. Zbl 1086.53085
Chow, Bennett; Knopf, Dan
261
2004
An example of neckpinching for Ricci flow on \(S^{n+1}\). Zbl 1064.58022
Angenent, Sigurd; Knopf, Dan
31
2004
Rotationally symmetric shrinking and expanding gradient Kähler-Ricci solitons. Zbl 1069.53036
Feldman, Mikhail; Ilmanen, Tom; Knopf, Dan
101
2003
A lower bound for the diameter of solutions to the Ricci flow with nonzero \(H^1(M^n, \mathbb R)\). Zbl 1048.58022
Ilmanen, Tom; Knopf, Dan
12
2003
Stability of the Ricci flow at Ricci-flat metrics. Zbl 1028.53043
Guenther, Christine; Isenberg, James; Knopf, Dan
32
2002
New Li-Yau-Hamilton inequalities for the Ricci flow via the space-time approach. Zbl 1048.53026
Chow, Bennett; Knopf, Dan
9
2002
Hamilton’s injectivity radius estimate for sequences with almost nonnegative curvature operators. Zbl 1041.53042
Chow, Bennett; Knopf, Dan; Lu, Peng
2
2002
Quasi-convergence of model geometries under the Ricci flow. Zbl 1020.53044
Knopf, Dan; McLeod, Kevin
16
2001
Quasi-convergence of the Ricci flow. Zbl 1027.53075
Knopf, Dan
6
2000
all top 5

Cited by 668 Authors

14 Ma, Li
12 Isenberg, James A.
12 Knopf, Dan
11 Azami, Shahroud
11 Cao, Huai-Dong
11 Wu, Jiayong
10 García-Río, Eduardo
10 Lu, Peng
9 Cao, Xiaodong
9 Lee, Man-Chun
9 Zhang, Yongjia
8 Abolarinwa, Abimbola
8 Chow, Bennett
8 Deruelle, Alix
8 Sharma, Ramesh
8 Topping, Peter Miles
7 Bamler, Richard H.
7 Ghosh, Amalendu
7 Mantegazza, Carlo
7 Streets, Jeffrey D.
7 Suh, Young Jin
7 Wang, Linfeng
7 Zhang, Qi-Shuhuason
7 Zhu, Anqiang
6 Baltazar, Halyson I.
6 Chan, Pak-Yeung
6 Cheng, Liang
6 Cho, Jong Taek
6 De, Uday Chand
6 Gang, Zhou
6 Guenther, Christine M.
6 Guo, Hongxin
6 Haslhofer, Robert
6 Šešum, Nataša
6 Wu, Guoqiang
6 Wu, Haotian
6 Zhang, Zhou
5 Cabezas-Rivas, Esther
5 Carfora, Mauro
5 Catino, Giovanni
5 Colding, Tobias Holck
5 Collins, Tristan Clifford
5 Fernández-López, Manuel
5 Kröncke, Klaus
5 Lott, John
5 Lüst, Dieter
5 Ma, Zilu
5 Minicozzi, William Philip II
5 Munteanu, Ovidiu
5 Stepanov, Sergeĭ Evgen’evich
5 Tam, Luen-Fai
5 Tian, Gang
5 Tosatti, Valentino
5 Wylie, William C.
5 Yan, Zaili
4 Buzano, Reto
4 Chen, Chih-Wei
4 Chen, Xiuxiong
4 De Biasio, Davide
4 Gianniotis, Panagiotis
4 Gomes, José Nazareno Vieira
4 Hou, Songbo
4 Kotschwar, Brett L.
4 Lakzian, Sajjad
4 Li, Yu
4 Loi, Andrea
4 Philipowski, Robert
4 Pulemotov, Artem
4 Razavi, Asadollah
4 Simon, Miles
4 Wang, Jianhong
4 Wang, Jiaping
4 Xu, Guoyi
4 Yang, Bo
4 Yildiz, Ahmet
4 Zhang, Zhenlei
3 Bahuaud, Eric
3 Batista, Rondinelle Marcolino
3 Bidabad, Behroz
3 Brendle, Simon
3 Conlon, Ronan J.
3 Coulibaly-Pasquier, Koléhè Abdoulaye
3 Di Giovanni, Francesco
3 Giesen, Gregor
3 Glickenstein, David
3 Hall, Stuart James
3 He, Fei
3 Hsu, Shu-Yu
3 Kimura, Makoto
3 Kleiner, Bruce
3 Kunikawa, Keita
3 Lafuente, Ramiro A.
3 Lasso Andino, Óscar
3 Lauret, Jorge
3 Li, Haozhao
3 Li, Xiang-Dong
3 Li, Yi
3 Mandal, Krishanu
3 Mazzieri, Lorenzo
3 Naik, Devaraja Mallesha
...and 568 more Authors
all top 5

Cited in 186 Serials

67 The Journal of Geometric Analysis
36 Proceedings of the American Mathematical Society
29 Calculus of Variations and Partial Differential Equations
21 Transactions of the American Mathematical Society
20 Advances in Mathematics
20 Journal of Functional Analysis
20 Mathematische Annalen
18 Annals of Global Analysis and Geometry
16 Journal of Geometry and Physics
15 Journal für die Reine und Angewandte Mathematik
15 Geometry & Topology
12 Geometriae Dedicata
12 Mathematische Zeitschrift
12 Differential Geometry and its Applications
10 Journal of Mathematical Physics
9 Journal of Mathematical Analysis and Applications
9 Geometric and Functional Analysis. GAFA
9 Comptes Rendus. Mathématique. Académie des Sciences, Paris
7 Journal of Geometry
7 Manuscripta Mathematica
7 Results in Mathematics
7 International Journal of Geometric Methods in Modern Physics
6 Inventiones Mathematicae
6 Journal of the Korean Mathematical Society
6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
6 Chinese Annals of Mathematics. Series B
6 Communications in Partial Differential Equations
6 Journal of High Energy Physics
5 Annali di Matematica Pura ed Applicata. Serie Quarta
5 Journal of Differential Geometry
5 Pacific Journal of Mathematics
5 Science China. Mathematics
4 Communications in Mathematical Physics
4 Communications on Pure and Applied Mathematics
4 Mathematical Notes
4 Duke Mathematical Journal
4 Mathematische Nachrichten
4 Mediterranean Journal of Mathematics
3 Classical and Quantum Gravity
3 Letters in Mathematical Physics
3 Ukrainian Mathematical Journal
3 Annales de l’Institut Fourier
3 Journal of the London Mathematical Society. Second Series
3 Memoirs of the American Mathematical Society
3 Monatshefte für Mathematik
3 Osaka Journal of Mathematics
3 Tôhoku Mathematical Journal. Second Series
3 Bulletin of the Iranian Mathematical Society
3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
3 International Journal of Mathematics
3 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
3 Potential Analysis
3 Journal of the European Mathematical Society (JEMS)
3 Communications of the Korean Mathematical Society
3 DGDS. Differential Geometry – Dynamical Systems
3 Advances in Geometry
3 Journal of Evolution Equations
3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
3 Journal of Fixed Point Theory and Applications
3 Frontiers of Mathematics in China
3 European Journal of Mathematics
2 Indian Journal of Pure & Applied Mathematics
2 Journal of Computational Physics
2 Nuclear Physics. B
2 Reports on Mathematical Physics
2 Beiträge zur Algebra und Geometrie
2 Fortschritte der Physik
2 Acta Mathematica
2 Kyungpook Mathematical Journal
2 Siberian Mathematical Journal
2 Bulletin of the Korean Mathematical Society
2 Note di Matematica
2 Journal of the American Mathematical Society
2 Annals of Physics
2 Journal de Mathématiques Pures et Appliquées. Neuvième Série
2 Stochastic Processes and their Applications
2 Bulletin of the American Mathematical Society. New Series
2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
2 Russian Mathematics
2 International Journal of Modern Physics D
2 Turkish Journal of Mathematics
2 Annales Academiae Scientiarum Fennicae. Mathematica
2 Annals of Mathematics. Second Series
2 Acta Mathematica Sinica. English Series
2 Communications in Contemporary Mathematics
2 Acta Mathematica Scientia. Series B. (English Edition)
2 JP Journal of Geometry and Topology
2 Boletim da Sociedade Paranaense de Matemática. Terceira Série
2 Journal of Mathematical Physics, Analysis, Geometry
2 International Electronic Journal of Geometry
2 Analysis and Mathematical Physics
2 Afrika Matematika
2 Axioms
2 Analysis and Geometry in Metric Spaces
2 Complex Manifolds
2 Transactions of the American Mathematical Society. Series B
1 International Journal of Modern Physics A
1 Analysis Mathematica
1 Archive for Rational Mechanics and Analysis
1 Bulletin of the Australian Mathematical Society
...and 86 more Serials
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Cited in 40 Fields

638 Differential geometry (53-XX)
166 Partial differential equations (35-XX)
160 Global analysis, analysis on manifolds (58-XX)
47 Several complex variables and analytic spaces (32-XX)
30 Relativity and gravitational theory (83-XX)
27 Quantum theory (81-XX)
26 Manifolds and cell complexes (57-XX)
17 Algebraic geometry (14-XX)
11 Dynamical systems and ergodic theory (37-XX)
11 Probability theory and stochastic processes (60-XX)
10 Topological groups, Lie groups (22-XX)
8 Calculus of variations and optimal control; optimization (49-XX)
6 Functions of a complex variable (30-XX)
6 Functional analysis (46-XX)
6 Numerical analysis (65-XX)
6 Fluid mechanics (76-XX)
4 Operator theory (47-XX)
4 Mechanics of particles and systems (70-XX)
3 Real functions (26-XX)
3 Geometry (51-XX)
3 Convex and discrete geometry (52-XX)
3 Computer science (68-XX)
3 Statistical mechanics, structure of matter (82-XX)
2 History and biography (01-XX)
2 Combinatorics (05-XX)
2 Number theory (11-XX)
2 Measure and integration (28-XX)
2 Potential theory (31-XX)
2 Ordinary differential equations (34-XX)
2 Astronomy and astrophysics (85-XX)
1 Nonassociative rings and algebras (17-XX)
1 Group theory and generalizations (20-XX)
1 Special functions (33-XX)
1 Difference and functional equations (39-XX)
1 Approximations and expansions (41-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 General topology (54-XX)
1 Operations research, mathematical programming (90-XX)
1 Biology and other natural sciences (92-XX)
1 Systems theory; control (93-XX)

Citations by Year