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## Colding, Tobias Holck

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 Author ID: colding.tobias-holck Published as: Colding, Tobias H.; Colding, Tobias Holck; Colding, T. H. Homepage: http://math.mit.edu/directory/profile.php?pid=50 External Links: MGP · Wikidata · GND · IdRef
 Documents Indexed: 86 Publications since 1995, including 2 Books
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#### Co-Authors

 8 single-authored 57 Minicozzi, William Philip II 8 Cheeger, Jeff 3 De Lellis, Camillo 3 Naber, Aaron C. 2 Gabai, David 2 Hingston, Nancy 2 Ilmanen, Thomas 2 Tian, Gang 1 Cai, Mingliang 1 Ketover, Daniel 1 Pedersen, Erik Kjær 1 Kleiner, Bruce 1 Minicozzi, William P. III 1 White, Brian Cabell 1 Yang, DaGang
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#### Serials

 12 Annals of Mathematics. Second Series 5 Communications on Pure and Applied Mathematics 5 Inventiones Mathematicae 5 Journal of Differential Geometry 4 Duke Mathematical Journal 4 IMRN. International Mathematics Research Notices 3 Geometric and Functional Analysis. GAFA 3 Comptes Rendus de l’Académie des Sciences. Série I 3 Notices of the American Mathematical Society 2 Commentarii Mathematici Helvetici 2 Publications Mathématiques 2 Proceedings of the National Academy of Sciences of the United States of America 2 Bulletin of the American Mathematical Society. New Series 2 Calculus of Variations and Partial Differential Equations 2 Mathematical Research Letters 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Geometry & Topology 1 Communications in Mathematical Physics 1 Acta Mathematica 1 Advances in Mathematics 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Bulletin of the London Mathematical Society 1 Geometriae Dedicata 1 Journal für die Reine und Angewandte Mathematik 1 Proceedings of the American Mathematical Society 1 Topology 1 Transactions of the American Mathematical Society 1 Journal of the American Mathematical Society 1 Electronic Research Announcements of the American Mathematical Society 1 Documenta Mathematica 1 The Journal of Symplectic Geometry 1 Graduate Studies in Mathematics 1 Courant Lecture Notes in Mathematics 1 ICCM Notices
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#### Fields

 77 Differential geometry (53-XX) 29 Global analysis, analysis on manifolds (58-XX) 12 Partial differential equations (35-XX) 8 Calculus of variations and optimal control; optimization (49-XX) 5 Manifolds and cell complexes (57-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 General and overarching topics; collections (00-XX) 1 Algebraic geometry (14-XX) 1 Potential theory (31-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX)

#### Citations contained in zbMATH Open

81 Publications have been cited 2,079 times in 990 Documents Cited by Year
On the structure of spaces with Ricci curvature bounded below. I. Zbl 0902.53034
Cheeger, Jeff; Colding, Tobias H.
1997
Generic mean curvature flow. I: Generic singularities. Zbl 1239.53084
Colding, Tobias H.; Minicozzi, William P. II
2012
Lower bounds on Ricci curvature and the almost rigidity of warped products. Zbl 0865.53037
Cheeger, Jeff; Colding, Tobias H.
1996
On the structure of spaces with Ricci curvature bounded below. III. Zbl 1027.53043
Cheeger, Jeff; Colding, Tobias H.
2000
On the structure of spaces with Ricci curvature bounded below. II. Zbl 1027.53042
Cheeger, Jeff; Colding, Tobias H.
2000
Ricci curvature and volume convergence. Zbl 0879.53030
Colding, Tobias H.
1997
A course in minimal surfaces. Zbl 1242.53007
Colding, Tobias Holck; Minicozzi, William P. II
2011
Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications. Zbl 1260.53067
Colding, Tobias Holck; Naber, Aaron
2012
On the singularities of spaces with bounded Ricci curvature. Zbl 1030.53046
Cheeger, J.; Colding, T. H.; Tian, G.
2002
Harmonic functions on manifolds. Zbl 0928.53030
Colding, Tobias H.; Minicozzi, William P. II
1997
The Calabi-Yau conjectures for embedded surfaces. Zbl 1142.53012
Colding, Tobias H.; Minicozzi, William P.
2008
The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV: Locally simply connected. Zbl 1076.53069
Colding, Tobias H.; Minicozzi, William P. II
2004
The min-max construction of minimal surfaces. Zbl 1051.53052
Colding, Tobias H.; De Lellis, Camillo
2003
Smooth compactness of self-shrinkers. Zbl 1258.53069
Colding, Tobias H.; Minicozzi, William P. II
2012
The space of embedded minimal surfaces of fixed genus in a 3-manifold. II: Multi-valued graphs in disks. Zbl 1070.53032
Colding, Tobias H.; Minicozzi, William P. II
2004
The space of embedded minimal surfaces of fixed genus in a 3-manifold. I: Estimates off the axis for disks. Zbl 1070.53031
Colding, Tobias H.; Minicozzi, William P. II
2004
Shape of manifolds with positive Ricci curvature. Zbl 0871.53027
Colding, Tobias H.
1996
Lower bounds for nodal sets of eigenfunctions. Zbl 1238.58020
Colding, Tobias H.; Minicozzi, William P. II
2011
Width and finite extinction time of Ricci flow. Zbl 1161.53352
Colding, Tobias H.; Minicozzi, William P. II
2008
Large manifolds with positive Ricci curvature. Zbl 0871.53028
Colding, Tobias H.
1996
Harmonic functions with polynomial growth. Zbl 0914.53027
Colding, Tobias H.; Minicozzi, William P. II
1997
Minimal surfaces. Zbl 0987.49025
Colding, Tobias H.; Minicozzi, William P. II
1999
The space of embedded minimal surfaces of fixed genus in a 3-manifold. III: Planar domains. Zbl 1076.53068
Colding, Tobias H.; Minicozzi, William P. II
2004
Liouville theorems for harmonic sections and applications. Zbl 0928.58022
Colding, Tobias H.; Minicozzi, William P. II
1998
Mean curvature flow. Zbl 1442.53064
Colding, Tobias Holck; Minicozzi, William P. II; Pedersen, Erik Kjær
2015
Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman. Zbl 1083.53058
Colding, Tobias H.; Minicozzi, William P. II
2005
Uniqueness of blowups and Łojasiewicz inequalities. Zbl 1337.53082
Colding, Tobias Holck; Minicozzi, William P. II
2015
The round sphere minimizes entropy among closed self-shrinkers. Zbl 1278.53069
Colding, Tobias Holck; Ilmanen, Tom; Minicozzi, William P. II.; White, Brian
2013
On uniqueness of tangent cones for Einstein manifolds. Zbl 1302.53048
Colding, Tobias Holck; Ii, William P. Minicozzi
2014
Weyl type bounds for harmonic functions. Zbl 0919.31004
Colding, Tobias H.; Minicozzi, William P. II
1998
Shapes of embedded minimal surfaces. Zbl 1175.53008
Colding, Tobias H.; Minicozzi, William P. II
2006
The space of embedded minimal surfaces of fixed genus in a 3-manifold. V. Fixed genus. Zbl 1322.53059
Colding, Tobias H.; Minicozzi, William P. II.
2015
Large scale behavior of kernels of Schrödinger operators. Zbl 0897.58041
Colding, Tobias H.; Minicozzi, William P. II
1997
Rigidity of generic singularities of mean curvature flow. Zbl 1331.53098
Colding, Tobias Holck; Ilmanen, Tom; Minicozzi, William P.
2015
Estimates for parametric elliptic integrands. Zbl 1002.53035
Colding, Tobias H.; Minicozzi, William P. II
2002
New monotonicity formulas for Ricci curvature and applications. I. Zbl 1277.53066
Colding, Tobias Holck
2012
Embedded minimal disks: Proper versus nonproper – global versus local. Zbl 1046.53001
Colding, Tobias H.; Minicozzi, William P. II
2004
An excursion into geometric analysis. Zbl 1076.53001
Colding, Tobias H.; Minicozzi, William P. II
2004
Characterization of tangent cones of noncollapsed limits with lower Ricci bounds and applications. Zbl 1271.53042
Colding, Tobias Holck; Naber, Aaron
2013
The singular set of mean curvature flow with generic singularities. Zbl 1341.53098
Colding, Tobias Holck; Minicozzi, William P. II
2016
Linear growth harmonic functions on complete manifolds with nonnegative Ricci curvature. Zbl 0871.53032
Cheeger, J.; Colding, T. H.; Minicozzi, W. P. II
1995
Width and mean curvature flow. Zbl 1165.53363
Colding, Tobias H.; Minicozzi, William P. II
2008
Monotonicity and its analytic and geometric implications. Zbl 1292.35002
Colding, Tobias Holck; Minicozzi, William P. II
2013
Almost rigidity of warped products and the structure of spaces with Ricci curvature bounded below. Zbl 0840.53024
Cheeger, Jeff; Colding, Tobias H.
1995
Sharp estimates for mean corvature flow of graphs. Zbl 1057.53050
Colding, Tobias H.; Minicozzi, William P. II
2004
Ricci curvature and monotonicity for harmonic functions. Zbl 1288.53028
Colding, Tobias Holck; Minicozzi, William P. II
2014
Embedded minimal surfaces without area bounds in 3-manifolds. Zbl 0999.53006
Colding, Tobias H.; Minicozzi, William P. II
2000
Multivalued minimal graphs and properness of disks. Zbl 1008.58012
Colding, Tobias H.; Minicozzi, William P. II
2002
Differentiability of the arrival time. Zbl 1353.53068
Colding, Tobias Holck; Minicozzi, William P. II
2016
Singular limit laminations, Morse index, and positive scalar curvature. Zbl 1096.53037
Colding, Tobias H.; De Lellis, Camillo
2005
Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications. Zbl 1170.35035
Colding, Tobias H.; Minicozzi II, William P.; De Lellis, Camillo
2008
Łojasiewicz inequalities and applications. Zbl 1329.53092
Colding, Tobias Holck; Minicozzi, William P. II
2015
Constraints on singularities under Ricci curvature bounds. Zbl 0876.53018
Cheeger, Jeff; Colding, Tobias H.; Tian, Gang
1997
Lower Ricci curvature, branching and the bilipschitz structure of uniform Reifenberg spaces. Zbl 1288.53031
Colding, Tobias Holck; Naber, Aaron
2013
Convergence of embedded minimal surfaces without area bounds in three-manifolds. Zbl 0918.53002
Colding, Tobias H.; Minicozzi II, William P.
1998
Complete properly embedded minimal surfaces in $$\mathbf R^3$$. Zbl 1010.49025
Colding, Tobias H.; Minicozzi, William P. II
2001
Level set method for motion by mean curvature. Zbl 1355.53057
Colding, Tobias Holck; Minicozzi, William P. II
2016
Examples of embedded minimal tori without area bounds. Zbl 0980.53084
Colding, Tobias H.; Minicozzi, William P. II
1999
Disks that are double spiral staircases. Zbl 1100.53008
Colding, Tobias H.; Minicozzi, William P. II
2003
Geodesic laminations with closed ends on surfaces and Morse index; Kupka-Smale metrics. Zbl 1095.53028
Colding, Tobias H.; Hingston, Nancy
2006
Minimal submanifolds. Zbl 1111.53007
Colding, Tobias H.; Minicozzi, William P. II
2006
Spaces with Ricci curvature bounds. Zbl 0955.53020
Colding, Tobias H.
1998
Minimal surfaces and mean curvature flow. Zbl 1261.53006
Colding, Tobias H.; Minicozzi, William P. II
2011
Generalized Liouville properties of manifolds. Zbl 0884.58032
Colding, Tobias H.; Minicozzi, William P.
1996
Singularity structure in mean curvature flow of mean-convex sets. Zbl 1071.53535
Colding, Tobias H.; Kleiner, Bruce
2003
Arnold-Thom gradient conjecture for the arrival time. Zbl 1441.35132
Colding, Tobias Holck; Minicozzi, William P. II
2019
Liouville properties. Zbl 07089920
Colding, Tobias H.; Minicozzi, William P.
2019
Regularity of the level set flow. Zbl 06866680
Colding, Tobias Holck; Minicozzi, William P. II
2018
On the classification of Heegaard splittings. Zbl 1403.57013
Colding, Tobias Holck; Gabai, David; Ketover, Daniel
2018
Minimal annuli with and without slits. Zbl 1087.53008
Colding, Tobias H.; Minicozzi, William P. II
2001
Metrics without Morse index bounds. Zbl 1059.53037
Colding, Tobias H.; Hingston, Nancy
2003
A gap theorem for ends of complete manifolds. Zbl 0827.53036
Cai, Mingliang; Colding, Tobias Holck; Yang, DaGang
1995
On the structure of embedded minimal annuli. Zbl 1122.53300
Colding, Tobias H.; Minicozzi, William P. II
2002
Embedded minimal disks. Zbl 1109.53008
Colding, Tobias H.; Minicozzi, William P. II
2005
Sharp frequency bounds for eigenfunctions of the Ornstein-Uhlenbeck operator. Zbl 1401.35219
Colding, Tobias Holck; Minicozzi, William P. II
2018
Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds. Zbl 1403.57012
Colding, Tobias Holck; Gabai, David
2018
In search of stable geometric structures. Zbl 1465.53005
Colding, Tobias Holck; Minicozzi, William P. III
2019
Volumes for eigensections. Zbl 1046.53022
Colding, Tobias H.; Minicozzi, William P. II
2003
Stability and Ricci curvature. Zbl 0830.53035
Colding, Tobias H.
1995
On function theory on spaces with a lower Ricci curvature bound. Zbl 0849.53034
Colding, Tobias H.; Minicozzi, William P. II
1996
Complexity of parabolic systems. Zbl 1458.53095
Colding, Tobias Holck; Minicozzi, William P.
2020
Complexity of parabolic systems. Zbl 1458.53095
Colding, Tobias Holck; Minicozzi, William P.
2020
Arnold-Thom gradient conjecture for the arrival time. Zbl 1441.35132
Colding, Tobias Holck; Minicozzi, William P. II
2019
Liouville properties. Zbl 07089920
Colding, Tobias H.; Minicozzi, William P.
2019
In search of stable geometric structures. Zbl 1465.53005
Colding, Tobias Holck; Minicozzi, William P. III
2019
Regularity of the level set flow. Zbl 06866680
Colding, Tobias Holck; Minicozzi, William P. II
2018
On the classification of Heegaard splittings. Zbl 1403.57013
Colding, Tobias Holck; Gabai, David; Ketover, Daniel
2018
Sharp frequency bounds for eigenfunctions of the Ornstein-Uhlenbeck operator. Zbl 1401.35219
Colding, Tobias Holck; Minicozzi, William P. II
2018
Effective finiteness of irreducible Heegaard splittings of non-Haken 3-manifolds. Zbl 1403.57012
Colding, Tobias Holck; Gabai, David
2018
The singular set of mean curvature flow with generic singularities. Zbl 1341.53098
Colding, Tobias Holck; Minicozzi, William P. II
2016
Differentiability of the arrival time. Zbl 1353.53068
Colding, Tobias Holck; Minicozzi, William P. II
2016
Level set method for motion by mean curvature. Zbl 1355.53057
Colding, Tobias Holck; Minicozzi, William P. II
2016
Mean curvature flow. Zbl 1442.53064
Colding, Tobias Holck; Minicozzi, William P. II; Pedersen, Erik Kjær
2015
Uniqueness of blowups and Łojasiewicz inequalities. Zbl 1337.53082
Colding, Tobias Holck; Minicozzi, William P. II
2015
The space of embedded minimal surfaces of fixed genus in a 3-manifold. V. Fixed genus. Zbl 1322.53059
Colding, Tobias H.; Minicozzi, William P. II.
2015
Rigidity of generic singularities of mean curvature flow. Zbl 1331.53098
Colding, Tobias Holck; Ilmanen, Tom; Minicozzi, William P.
2015
Łojasiewicz inequalities and applications. Zbl 1329.53092
Colding, Tobias Holck; Minicozzi, William P. II
2015
On uniqueness of tangent cones for Einstein manifolds. Zbl 1302.53048
Colding, Tobias Holck; Ii, William P. Minicozzi
2014
Ricci curvature and monotonicity for harmonic functions. Zbl 1288.53028
Colding, Tobias Holck; Minicozzi, William P. II
2014
The round sphere minimizes entropy among closed self-shrinkers. Zbl 1278.53069
Colding, Tobias Holck; Ilmanen, Tom; Minicozzi, William P. II.; White, Brian
2013
Characterization of tangent cones of noncollapsed limits with lower Ricci bounds and applications. Zbl 1271.53042
Colding, Tobias Holck; Naber, Aaron
2013
Monotonicity and its analytic and geometric implications. Zbl 1292.35002
Colding, Tobias Holck; Minicozzi, William P. II
2013
Lower Ricci curvature, branching and the bilipschitz structure of uniform Reifenberg spaces. Zbl 1288.53031
Colding, Tobias Holck; Naber, Aaron
2013
Generic mean curvature flow. I: Generic singularities. Zbl 1239.53084
Colding, Tobias H.; Minicozzi, William P. II
2012
Sharp Hölder continuity of tangent cones for spaces with a lower Ricci curvature bound and applications. Zbl 1260.53067
Colding, Tobias Holck; Naber, Aaron
2012
Smooth compactness of self-shrinkers. Zbl 1258.53069
Colding, Tobias H.; Minicozzi, William P. II
2012
New monotonicity formulas for Ricci curvature and applications. I. Zbl 1277.53066
Colding, Tobias Holck
2012
A course in minimal surfaces. Zbl 1242.53007
Colding, Tobias Holck; Minicozzi, William P. II
2011
Lower bounds for nodal sets of eigenfunctions. Zbl 1238.58020
Colding, Tobias H.; Minicozzi, William P. II
2011
Minimal surfaces and mean curvature flow. Zbl 1261.53006
Colding, Tobias H.; Minicozzi, William P. II
2011
The Calabi-Yau conjectures for embedded surfaces. Zbl 1142.53012
Colding, Tobias H.; Minicozzi, William P.
2008
Width and finite extinction time of Ricci flow. Zbl 1161.53352
Colding, Tobias H.; Minicozzi, William P. II
2008
Width and mean curvature flow. Zbl 1165.53363
Colding, Tobias H.; Minicozzi, William P. II
2008
Three circles theorems for Schrödinger operators on cylindrical ends and geometric applications. Zbl 1170.35035
Colding, Tobias H.; Minicozzi II, William P.; De Lellis, Camillo
2008
Shapes of embedded minimal surfaces. Zbl 1175.53008
Colding, Tobias H.; Minicozzi, William P. II
2006
Geodesic laminations with closed ends on surfaces and Morse index; Kupka-Smale metrics. Zbl 1095.53028
Colding, Tobias H.; Hingston, Nancy
2006
Minimal submanifolds. Zbl 1111.53007
Colding, Tobias H.; Minicozzi, William P. II
2006
Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman. Zbl 1083.53058
Colding, Tobias H.; Minicozzi, William P. II
2005
Singular limit laminations, Morse index, and positive scalar curvature. Zbl 1096.53037
Colding, Tobias H.; De Lellis, Camillo
2005
Embedded minimal disks. Zbl 1109.53008
Colding, Tobias H.; Minicozzi, William P. II
2005
The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV: Locally simply connected. Zbl 1076.53069
Colding, Tobias H.; Minicozzi, William P. II
2004
The space of embedded minimal surfaces of fixed genus in a 3-manifold. II: Multi-valued graphs in disks. Zbl 1070.53032
Colding, Tobias H.; Minicozzi, William P. II
2004
The space of embedded minimal surfaces of fixed genus in a 3-manifold. I: Estimates off the axis for disks. Zbl 1070.53031
Colding, Tobias H.; Minicozzi, William P. II
2004
The space of embedded minimal surfaces of fixed genus in a 3-manifold. III: Planar domains. Zbl 1076.53068
Colding, Tobias H.; Minicozzi, William P. II
2004
Embedded minimal disks: Proper versus nonproper – global versus local. Zbl 1046.53001
Colding, Tobias H.; Minicozzi, William P. II
2004
An excursion into geometric analysis. Zbl 1076.53001
Colding, Tobias H.; Minicozzi, William P. II
2004
Sharp estimates for mean corvature flow of graphs. Zbl 1057.53050
Colding, Tobias H.; Minicozzi, William P. II
2004
The min-max construction of minimal surfaces. Zbl 1051.53052
Colding, Tobias H.; De Lellis, Camillo
2003
Disks that are double spiral staircases. Zbl 1100.53008
Colding, Tobias H.; Minicozzi, William P. II
2003
Singularity structure in mean curvature flow of mean-convex sets. Zbl 1071.53535
Colding, Tobias H.; Kleiner, Bruce
2003
Metrics without Morse index bounds. Zbl 1059.53037
Colding, Tobias H.; Hingston, Nancy
2003
Volumes for eigensections. Zbl 1046.53022
Colding, Tobias H.; Minicozzi, William P. II
2003
On the singularities of spaces with bounded Ricci curvature. Zbl 1030.53046
Cheeger, J.; Colding, T. H.; Tian, G.
2002
Estimates for parametric elliptic integrands. Zbl 1002.53035
Colding, Tobias H.; Minicozzi, William P. II
2002
Multivalued minimal graphs and properness of disks. Zbl 1008.58012
Colding, Tobias H.; Minicozzi, William P. II
2002
On the structure of embedded minimal annuli. Zbl 1122.53300
Colding, Tobias H.; Minicozzi, William P. II
2002
Complete properly embedded minimal surfaces in $$\mathbf R^3$$. Zbl 1010.49025
Colding, Tobias H.; Minicozzi, William P. II
2001
Minimal annuli with and without slits. Zbl 1087.53008
Colding, Tobias H.; Minicozzi, William P. II
2001
On the structure of spaces with Ricci curvature bounded below. III. Zbl 1027.53043
Cheeger, Jeff; Colding, Tobias H.
2000
On the structure of spaces with Ricci curvature bounded below. II. Zbl 1027.53042
Cheeger, Jeff; Colding, Tobias H.
2000
Embedded minimal surfaces without area bounds in 3-manifolds. Zbl 0999.53006
Colding, Tobias H.; Minicozzi, William P. II
2000
Minimal surfaces. Zbl 0987.49025
Colding, Tobias H.; Minicozzi, William P. II
1999
Examples of embedded minimal tori without area bounds. Zbl 0980.53084
Colding, Tobias H.; Minicozzi, William P. II
1999
Liouville theorems for harmonic sections and applications. Zbl 0928.58022
Colding, Tobias H.; Minicozzi, William P. II
1998
Weyl type bounds for harmonic functions. Zbl 0919.31004
Colding, Tobias H.; Minicozzi, William P. II
1998
Convergence of embedded minimal surfaces without area bounds in three-manifolds. Zbl 0918.53002
Colding, Tobias H.; Minicozzi II, William P.
1998
Spaces with Ricci curvature bounds. Zbl 0955.53020
Colding, Tobias H.
1998
On the structure of spaces with Ricci curvature bounded below. I. Zbl 0902.53034
Cheeger, Jeff; Colding, Tobias H.
1997
Ricci curvature and volume convergence. Zbl 0879.53030
Colding, Tobias H.
1997
Harmonic functions on manifolds. Zbl 0928.53030
Colding, Tobias H.; Minicozzi, William P. II
1997
Harmonic functions with polynomial growth. Zbl 0914.53027
Colding, Tobias H.; Minicozzi, William P. II
1997
Large scale behavior of kernels of Schrödinger operators. Zbl 0897.58041
Colding, Tobias H.; Minicozzi, William P. II
1997
Constraints on singularities under Ricci curvature bounds. Zbl 0876.53018
Cheeger, Jeff; Colding, Tobias H.; Tian, Gang
1997
Lower bounds on Ricci curvature and the almost rigidity of warped products. Zbl 0865.53037
Cheeger, Jeff; Colding, Tobias H.
1996
Shape of manifolds with positive Ricci curvature. Zbl 0871.53027
Colding, Tobias H.
1996
Large manifolds with positive Ricci curvature. Zbl 0871.53028
Colding, Tobias H.
1996
Generalized Liouville properties of manifolds. Zbl 0884.58032
Colding, Tobias H.; Minicozzi, William P.
1996
On function theory on spaces with a lower Ricci curvature bound. Zbl 0849.53034
Colding, Tobias H.; Minicozzi, William P. II
1996
Linear growth harmonic functions on complete manifolds with nonnegative Ricci curvature. Zbl 0871.53032
Cheeger, J.; Colding, T. H.; Minicozzi, W. P. II
1995
Almost rigidity of warped products and the structure of spaces with Ricci curvature bounded below. Zbl 0840.53024
Cheeger, Jeff; Colding, Tobias H.
1995
A gap theorem for ends of complete manifolds. Zbl 0827.53036
Cai, Mingliang; Colding, Tobias Holck; Yang, DaGang
1995
Stability and Ricci curvature. Zbl 0830.53035
Colding, Tobias H.
1995
all top 5

#### Cited by 912 Authors

 29 Colding, Tobias Holck 21 Minicozzi, William Philip II 17 Honda, Shouhei 16 Meeks, William Hamilton III 15 Gigli, Nicola 14 Alarcón, Antonio 14 Tian, Gang 12 Wei, Guofang 11 Cheeger, Jeff 11 Naber, Aaron C. 11 Zhou, Detang 10 Tinaglia, Giuseppe 9 Forstnerič, Franc 9 Lopez Fernandez, Francisco Jose 8 Bernstein, Jacob 8 Brendle, Simon 8 Chen, Xiuxiong 8 Cheng, Qingming 8 Hua, Bobo 8 Li, Chi 8 Mondino, Andrea 8 Zhou, Xin 7 Ambrosio, Luigi 7 Bamler, Richard H. 7 Cheng, Xu 7 Ding, Qi 7 Jost, Jürgen 7 Ma, Li 7 Martín, Francisco 7 Sormani, Christina 7 Sun, Song 7 Wang, Bing 7 Wang, Lu 6 Arroja Neves, André 6 Haslhofer, Robert 6 Jiang, Wenshuai 6 Kleene, Stephen James 6 Kleiner, Bruce 6 Li, Haizhong 6 Lin, Longzhi 6 Pérez Muñoz, Joaquín 6 Rimoldi, Michele 6 Rosenberg, Harold 6 Xia, Changyu 6 Xin, Yuanlong 6 Xu, Hongwei 6 Zhu, Jonathan J. H. 5 Coskunuzer, Baris 5 Guang, Qiang 5 Impera, Debora 5 Ketterer, Christian 5 Koskela, Pekka 5 Lott, John 5 Lu, Zhiqin 5 Marques, Fernando Codá 5 Portegies, Jacobus W. 5 Qiu, Hongbing 5 Rigoli, Marco 5 Rong, Xiaochun 5 Savaré, Giuseppe 5 Schulze, Felix 5 Székelyhidi, Gábor 5 Wei, Guoxin 5 Wei, Yong 5 Wu, Chuanxi 5 Xu, Guoyi 5 Zeng, Lingzhong 4 Anza Hafsa, Omar 4 Breiner, Christine 4 Case, Jeffrey S. 4 Charalambous, Nelia 4 Chen, Qing 4 Donaldson, Simon Kirwan 4 Du, Feng 4 Espinar, José María 4 Feehan, Paul M. N. 4 Hein, Hans-Joachim 4 Huang, Xian-Tao 4 Jiang, Renjin 4 Kitabeppu, Yu 4 Lamm, Tobias 4 Li, Haozhao 4 Li, Xingxiao 4 Li, Yu 4 Mandallena, Jean-Philippe 4 Mazzieri, Lorenzo 4 Munn, Michael 4 Petersen, Peter V 4 Pigola, Stefano 4 Rajala, Tapio 4 Schnürer, Oliver Christian 4 Shaikh, Absos Ali 4 Wang, Qiaoling 4 Xu, Chenyang 4 Zhang, Yuguang 4 Zhang, Zhenlei 4 Zhao, En-Tao 4 Zhu, Meng 4 Zhu, Yecheng 3 Adriano, Levi ...and 812 more Authors
all top 5

#### Cited in 164 Serials

 70 The Journal of Geometric Analysis 58 Calculus of Variations and Partial Differential Equations 52 Transactions of the American Mathematical Society 46 Proceedings of the American Mathematical Society 43 Journal für die Reine und Angewandte Mathematik 37 Advances in Mathematics 28 Journal of Functional Analysis 26 Mathematische Annalen 25 Geometriae Dedicata 25 Mathematische Zeitschrift 23 Differential Geometry and its Applications 23 Geometry & Topology 19 Duke Mathematical Journal 19 Inventiones Mathematicae 19 Annals of Mathematics. Second Series 17 Annals of Global Analysis and Geometry 16 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 16 Geometric and Functional Analysis. GAFA 14 Communications in Contemporary Mathematics 13 Journal of the American Mathematical Society 11 Journal of Mathematical Analysis and Applications 10 Communications on Pure and Applied Mathematics 10 Science China. Mathematics 9 Communications in Mathematical Physics 9 Journal of Differential Equations 9 Manuscripta Mathematica 9 Memoirs of the American Mathematical Society 9 Bulletin of the American Mathematical Society. New Series 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 8 Journal of Geometry and Physics 8 Acta Mathematica 8 Pacific Journal of Mathematics 8 Potential Analysis 8 Analysis and Geometry in Metric Spaces 7 Acta Mathematica Sinica. English Series 6 Annales de l’Institut Fourier 6 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 6 Revista Matemática Iberoamericana 6 Communications in Partial Differential Equations 6 Journal of the European Mathematical Society (JEMS) 6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 6 Frontiers of Mathematics in China 5 Archive for Rational Mechanics and Analysis 5 Israel Journal of Mathematics 5 Publications Mathématiques 5 Journal de Mathématiques Pures et Appliquées. Neuvième Série 5 Proceedings of the National Academy of Sciences of the United States of America 5 Discrete and Continuous Dynamical Systems 5 Annales Henri Poincaré 4 General Relativity and Gravitation 4 Journal of Geometry 4 International Journal of Mathematics 3 Bulletin of the Australian Mathematical Society 3 Archiv der Mathematik 3 Illinois Journal of Mathematics 3 Journal of the Mathematical Society of Japan 3 Monatshefte für Mathematik 3 Results in Mathematics 3 Chinese Annals of Mathematics. Series B 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Bulletin of the Brazilian Mathematical Society. New Series 3 Mediterranean Journal of Mathematics 3 Japanese Journal of Mathematics. 3rd Series 3 Forum of Mathematics, Sigma 2 Journal d’Analyse Mathématique 2 Journal of Mathematical Physics 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Arkiv för Matematik 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 The Annals of Probability 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Compositio Mathematica 2 Journal of Differential Geometry 2 Journal of the London Mathematical Society. Second Series 2 Mathematische Nachrichten 2 Proceedings of the London Mathematical Society. Third Series 2 Tohoku Mathematical Journal. Second Series 2 Topology and its Applications 2 Bulletin of the Korean Mathematical Society 2 Probability Theory and Related Fields 2 SIAM Journal on Mathematical Analysis 2 Journal of Mathematical Sciences (New York) 2 St. Petersburg Mathematical Journal 2 Bulletin des Sciences Mathématiques 2 Central European Journal of Mathematics 2 Analysis & PDE 2 Communications in Mathematics and Statistics 2 Bollettino dell’Unione Matematica Italiana 2 Peking Mathematical Journal 2 Annales Fennici Mathematici 1 American Mathematical Monthly 1 Applicable Analysis 1 Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV) 1 Journal of Computational Physics 1 Journal of Statistical Physics 1 Nonlinearity 1 Nuclear Physics. B 1 Physics Letters. A 1 Chaos, Solitons and Fractals 1 The Mathematical Intelligencer ...and 64 more Serials
all top 5

#### Cited in 47 Fields

 795 Differential geometry (53-XX) 214 Global analysis, analysis on manifolds (58-XX) 192 Partial differential equations (35-XX) 115 Calculus of variations and optimal control; optimization (49-XX) 65 Several complex variables and analytic spaces (32-XX) 62 Manifolds and cell complexes (57-XX) 39 Potential theory (31-XX) 36 Algebraic geometry (14-XX) 26 Functions of a complex variable (30-XX) 24 Probability theory and stochastic processes (60-XX) 21 Measure and integration (28-XX) 20 Functional analysis (46-XX) 16 Relativity and gravitational theory (83-XX) 15 Group theory and generalizations (20-XX) 15 Dynamical systems and ergodic theory (37-XX) 12 Topological groups, Lie groups (22-XX) 12 Geometry (51-XX) 11 Abstract harmonic analysis (43-XX) 8 Combinatorics (05-XX) 8 Operator theory (47-XX) 8 Convex and discrete geometry (52-XX) 8 General topology (54-XX) 8 Quantum theory (81-XX) 6 Harmonic analysis on Euclidean spaces (42-XX) 6 Statistical mechanics, structure of matter (82-XX) 5 Numerical analysis (65-XX) 5 Fluid mechanics (76-XX) 4 Ordinary differential equations (34-XX) 3 General and overarching topics; collections (00-XX) 3 Real functions (26-XX) 3 Operations research, mathematical programming (90-XX) 2 History and biography (01-XX) 2 Number theory (11-XX) 2 Algebraic topology (55-XX) 2 Mechanics of particles and systems (70-XX) 2 Mechanics of deformable solids (74-XX) 2 Astronomy and astrophysics (85-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Information and communication theory, circuits (94-XX) 1 Commutative algebra (13-XX) 1 Special functions (33-XX) 1 Approximations and expansions (41-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Optics, electromagnetic theory (78-XX) 1 Biology and other natural sciences (92-XX) 1 Mathematics education (97-XX)

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