## Cheeger, Jeff

Compute Distance To:
 Author ID: cheeger.jeff Published as: Cheeger, Jeff; Cheeger, J.; Cheeger, Jeffrey more...less Homepage: https://math.nyu.edu/people/profiles/CHEEGER_Jeff.html External Links: MGP · Wikidata · dblp · GND · IdRef Awards: Shaw Prize (2021)
 Documents Indexed: 95 Publications since 1968, including 3 Books 1 Contribution as Editor Biographic References: 5 Publications Co-Authors: 38 Co-Authors with 70 Joint Publications 1,137 Co-Co-Authors
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### Co-Authors

 26 single-authored 11 Kleiner, Bruce 10 Gromov, Mikhael Leonidovich 8 Bismut, Jean-Michel 8 Colding, Tobias Holck 7 Naber, Aaron C. 5 Tian, Gang 4 Ebin, David G. 4 Gromoll, Detlef 4 Rong, Xiaochun 3 Müller, Werner 3 Simons, James 3 Taylor, Michael Eugene 2 Anderson, Michael T. 2 Bryant, Robert L. 2 Cao, Jianguo 2 Griffiths, Phillip Augustus 2 Grove, Karsten 2 Haslhofer, Robert 2 Naor, Assaf 2 Schrader, Robert 1 Baum, Paul Frank 1 Besson, Gérard 1 Blum, Lenore 1 Bourguignon, Jean-Pierre 1 Burns, Daniel M. jun. 1 Connes, Alain 1 Dai, Xianzhe 1 Donaldson, Simon Kirwan 1 Donnelly, Harold 1 Fukaya, Kenji 1 Goresky, Robert Mark 1 Guillemin, Victor W. 1 Jiang, Wenshuai 1 Kazdan, Jerry L. 1 Kister, James M. 1 Lafontaine, Jacques 1 Lawson, Herbert Blaine jun. 1 LeBrun, Claude R. 1 MacPherson, Robert Duncan 1 Marcus, Adam W. 1 Michelsohn, Marie-Louise 1 Minicozzi, William Philip II 1 Nigel Hitchin 1 Palais, Richard S. 1 Pansu, Pierre 1 Rossi, Hugo 1 Schioppa, Andrea 1 Singer, Elliot 1 Singer, Isadore Manuel 1 Singer, Natasha 1 Spielman, Daniel Alan 1 Srivastava, Nikhil 1 Stanton, Nancy K. 1 Sternberg, Shlomo 1 Sullivan, Dennis Parnell 1 Valtorta, Daniele 1 Witten, Edward 1 Yau, Shing-Tung
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### Serials

 13 Journal of Differential Geometry 10 Geometric and Functional Analysis. GAFA 6 Communications on Pure and Applied Mathematics 6 Annals of Mathematics. Second Series 4 Inventiones Mathematicae 4 Comptes Rendus de l’Académie des Sciences. Série I 3 Topology 3 Journal of the American Mathematical Society 3 Notices of the American Mathematical Society 2 Communications in Mathematical Physics 2 American Journal of Mathematics 2 Journal of Functional Analysis 2 Proceedings of the National Academy of Sciences of the United States of America 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 2 Analysis and Geometry in Metric Spaces 1 Acta Mathematica 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Archiv der Mathematik 1 Indiana University Mathematics Journal 1 Communications in Analysis and Geometry 1 Calculus of Variations and Partial Differential Equations 1 Milan Journal of Mathematics 1 Bulletin of the American Mathematical Society 1 North-Holland Mathematical Library 1 Surveys in Differential Geometry
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### Fields

 57 Differential geometry (53-XX) 36 Global analysis, analysis on manifolds (58-XX) 14 Manifolds and cell complexes (57-XX) 8 Partial differential equations (35-XX) 8 Functional analysis (46-XX) 6 Algebraic topology (55-XX) 5 Functions of a complex variable (30-XX) 3 History and biography (01-XX) 3 Topological groups, Lie groups (22-XX) 3 Real functions (26-XX) 3 Several complex variables and analytic spaces (32-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 2 Algebraic geometry (14-XX) 2 Group theory and generalizations (20-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Number theory (11-XX) 1 Measure and integration (28-XX) 1 General topology (54-XX) 1 Computer science (68-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

91 Publications have been cited 5,448 times in 3,461 Documents Cited by Year
Comparison theorems in Riemannian geometry. Zbl 0309.53035
Cheeger, Jeff; Ebin, David G.
1975
Differentiability of Lipschitz functions on metric measure spaces. Zbl 0942.58018
Cheeger, J.
1999
Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. Zbl 0493.53035
Cheeger, Jeff; Gromov, Mikhail; Taylor, Michael
1982
On the structure of complete manifolds of nonnegative curvature. Zbl 0246.53049
Cheeger, Jeff; Gromoll, Detlef
1972
On the structure of spaces with Ricci curvature bounded below. I. Zbl 0902.53034
Cheeger, Jeff; Colding, Tobias H.
1997
Lower bounds on Ricci curvature and the almost rigidity of warped products. Zbl 0865.53037
Cheeger, Jeff; Colding, Tobias H.
1996
The splitting theorem for manifolds of nonnegative Ricci curvature. Zbl 0223.53033
Cheeger, Jeff; Gromoll, Detlef
1971
A lower bound for the smallest eigenvalue of the Laplacian. Zbl 0212.44903
Cheeger, J.
1970
Spectral geometry of singular Riemannian spaces. Zbl 0529.58034
Cheeger, Jeff
1983
On the structure of spaces with Ricci curvature bounded below. III. Zbl 1027.53043
Cheeger, Jeff; Colding, Tobias H.
2000
Analytic torsion and the heat equation. Zbl 0412.58026
Cheeger, Jeff
1979
Finiteness theorems for Riemannian manifolds. Zbl 0194.52902
Cheeger, J.
1970
On the structure of spaces with Ricci curvature bounded below. II. Zbl 1027.53042
Cheeger, Jeff; Colding, Tobias H.
2000
On the spectral geometry of spaces with cone-like singularities. Zbl 0411.58003
Cheeger, Jeff
1979
Collapsing Riemannian manifolds while keeping their curvature bounded. I. Zbl 0606.53028
Cheeger, Jeff; Gromov, Mikhael
1986
A lower bound for the heat kernel. Zbl 0481.35003
Cheeger, Jeff; Yau, Shing-Tung
1981
$$L_ 2$$-cohomology and group cohomology. Zbl 0597.57020
Cheeger, Jeff; Gromov, Mikhael
1986
Differential characters and geometric invariants. Zbl 0621.57010
Cheeger, Jeff; Simons, James
1985
On the Hodge theory of Riemannian pseudomanifolds. Zbl 0461.58002
Cheeger, Jeff
1980
$$\eta$$-invariants and their adiabatic limits. Zbl 0671.58037
Bismut, Jean-Michel; Cheeger, Jeff
1989
Bounds on the von Neumann dimension of $$L^ 2$$-cohomoloy and the Gauss- Bonnet theorem for open manifolds. Zbl 0614.53034
Cheeger, Jeff; Gromov, Mikhael
1985
Nilpotent structures and invariant metrics on collapsed manifolds. Zbl 0758.53022
Cheeger, Jeff; Fukaya, Kenji; Gromov, Mikhael
1992
On the curvature of piecewise flat spaces. Zbl 0559.53028
Cheeger, Jeff; Müller, Werner; Schrader, Robert
1984
On the singularities of spaces with bounded Ricci curvature. Zbl 1030.53046
Cheeger, J.; Colding, T. H.; Tian, G.
2002
Some examples of manifolds of nonnegative curvature. Zbl 0281.53040
Cheeger, Jeff
1973
On the diffraction of waves by conical singularities. I. Zbl 0526.58049
Cheeger, Jeff; Taylor, Michael
1982
$$C^ \alpha$$-compactness for manifolds with Ricci curvature and injectivity radius bounded below. Zbl 0774.53021
Anderson, Michael T.; Cheeger, Jeff
1992
Collapsing Riemannian manifolds while keeping their curvature bounded. II. Zbl 0727.53043
Cheeger, Jeff; Gromov, Mikhael
1990
Comparison theorems in Riemannian geometry. Reprint of the 1975 original. Zbl 1142.53003
Cheeger, Jeff; Ebin, David G.
2008
Degeneration of Riemannian metrics under Ricci curvature bounds. Zbl 1055.53024
Cheeger, Jeff
2001
$$L^ 2-$$cohomology and intersection homology of singular algebraic varieties. Zbl 0503.14008
Cheeger, Jeff; Goresky, Mark; MacPherson, Robert
1982
Lower bounds on Ricci curvature and quantitative behavior of singular sets. Zbl 1268.53053
Cheeger, Jeff; Naber, Aaron
2013
On the diffraction of waves by conical singularities. II. Zbl 0536.58032
Cheeger, Jeff; Taylor, Michael
1982
Critical points of distance functions and applications to geometry. Zbl 0771.53015
Cheeger, Jeff
1991
Regularity of Einstein manifolds and the codimension 4 conjecture. Zbl 1335.53057
Cheeger, Jeff; Naber, Aaron
2015
Differentiating maps into $$L^1$$, and the geometry of BV functions. Zbl 1194.22009
Cheeger, Jeff; Kleiner, Bruce
2010
On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay. Zbl 0814.53034
Cheeger, Jeff; Tian, Gang
1994
On the characteristic numbers of complete manifolds of bounded curvature and finite volume. Zbl 0592.53036
Cheeger, Jeff; Gromov, Mikhael
1985
Critical sets of elliptic equations. Zbl 1309.35012
Cheeger, Jeff; Naber, Aaron; Valtorta, Daniele
2015
Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon-Nikodym property. Zbl 1200.58007
Cheeger, Jeff; Kleiner, Bruce
2009
Families index for manifolds with boundary, superconnections, and cones. I: Families of manifolds with boundary and Dirac operators. Zbl 0696.53021
Bismut, Jean-Michel; Cheeger, Jeff
1990
$$\eta$$-invariants, the adiabatic approximation and conical singularities. Zbl 0623.58021
Cheeger, Jeff
1987
Compression bounds for Lipschitz maps from the Heisenberg group to $$L_{1}$$. Zbl 1247.46020
Cheeger, Jeff; Kleiner, Bruce; Naor, Assaf
2011
On the differentiability of Lipschitz maps from metric measure spaces to Banach spaces. Zbl 1139.58004
Cheeger, Jeff; Kleiner, Bruce
2006
Diffeomorphism finiteness for manifolds with Ricci curvature and $$L^{n/2}$$-norm of curvature bounded. Zbl 0764.53026
Anderson, Michael T.; Cheeger, Jeff
1991
Quantitative stratification and the regularity of harmonic maps and minimal currents. Zbl 1269.53063
Cheeger, Jeff; Naber, Aaron
2013
Curvature and injectivity radius estimates for Einstein 4-manifolds. Zbl 1092.53034
Cheeger, Jeff; Tian, Gang
2006
Integral bounds on curvature, elliptic estimates and rectifiability of singular sets. Zbl 1086.53051
Cheeger, J.
2003
Metric differentiation, monotonicity and maps to $$L^{1}$$. Zbl 1214.46013
Cheeger, Jeff; Kleiner, Bruce
2010
Quantitative stratification and the regularity of mean curvature flow. Zbl 1277.53064
Cheeger, Jeff; Haslhofer, Robert; Naber, Aaron
2013
Analytic torsion and Reidemeister torsion. Zbl 0358.57005
Cheeger, Jeff
1977
Families index for manifolds with boundary, superconnections and cones. II: The Chern character. Zbl 0711.53023
Bismut, Jean-Michel; Cheeger, Jeff
1990
Realization of metric spaces as inverse limits, and bilipschitz embedding in $$L_1$$. Zbl 1277.46012
Cheeger, Jeff; Kleiner, Bruce
2013
Linear growth harmonic functions on complete manifolds with nonnegative Ricci curvature. Zbl 0871.53032
Cheeger, J.; Colding, T. H.; Minicozzi, W. P. II
1995
Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below. Zbl 1469.53083
Cheeger, Jeff; Jiang, Wenshuai; Naber, Aaron
2021
A $$(\log n)^{\Omega(1)}$$ integrality gap for the sparsest cut SDP. Zbl 1291.90318
Cheeger, Jeff; Kleiner, Bruce; Naor, Assaf
2009
Inverse limit spaces satisfying a Poincaré inequality. Zbl 1331.46016
Cheeger, Jeff; Kleiner, Bruce
2015
Chopping Riemannian manifolds. Zbl 0722.53045
Cheeger, Jeff; Gromov, Mikhael
1991
Kinematic and tube formulas for piecewise linear spaces. Zbl 0615.53058
Cheeger, J.; Müller, W.; Schrader, R.
1986
Counting topological manifolds. Zbl 0199.58403
Cheeger, J.; Kister, J. M.
1970
The relation between the Laplacian and the diameter for manifolds of non- negative curvature. Zbl 0177.50201
Cheeger, J.
1968
Degeneration of Einstein metrics and metrics with special holonomy. Zbl 1053.53028
Cheeger, Jeff
2003
Infinitesimal structure of differentiability spaces, and metric differentiation. Zbl 1360.30047
Cheeger, Jeff; Kleiner, Bruce; Schioppa, Andrea
2016
Almost rigidity of warped products and the structure of spaces with Ricci curvature bounded below. Zbl 0840.53024
Cheeger, Jeff; Colding, Tobias H.
1995
Quantitative stratification and the regularity of harmonic map flow. Zbl 1317.53081
Cheeger, Jeff; Haslhofer, Robert; Naber, Aaron
2015
The structure of complete manifolds of nonnegative curvature. Zbl 0169.24101
Cheeger, J.; Gromoll, D.
1968
Generalized differentiation and bi-Lipschitz nonembedding in $$L^{1}$$. Zbl 1100.58004
Cheeger, Jeff; Kleiner, Bruce
2006
Transgressed Euler classes of $$SL(2n,\mathbb{Z})$$ vector bundles, adiabatic limits of eta invariants and special values of $$L$$-functions. Zbl 0768.58048
Bismut, Jean-Michel; Cheeger, Jeff
1992
Quantitative differentiation: a general formulation. Zbl 1258.30027
Cheeger, Jeff
2012
Infinitesimal isometries and Pontryagin numbers. Zbl 0179.28802
Baum, P. F.; Cheeger, J.
1969
Pinching theorems for a certain class of Riemannian manifolds. Zbl 0183.50301
Cheeger, J.
1969
Anti-self-duality of curvature and degeneration of metrics with special holonomy. Zbl 1081.53038
Cheeger, Jeff; Tian, Gang
2005
On the lower bound for the injectivity radius of 1/4-pinched Riemannian manifolds. Zbl 0468.53035
Cheeger, Jeff; Gromoll, Detlef
1980
Constraints on singularities under Ricci curvature bounds. Zbl 0876.53018
Cheeger, Jeff; Colding, Tobias H.; Tian, Gang
1997
Existence of polarized $$F$$-structures on collapsed manifolds with bounded curvature and diameter. Zbl 0863.53026
Cheeger, J.; Rong, X.
1996
A combinatorial formula for Stiefel-Whitney classes. Zbl 0282.57009
Cheeger, Jeff
1971
Multiplication of differential characters. Zbl 0285.53014
Cheeger, Jeff
1973
Collapsed Riemannian manifolds with bounded diameter and bounded covering geometry. Zbl 0843.53039
Cheeger, J.; Rong, X.
1995
Hodge theory of complex cones. Zbl 0583.58004
Cheeger, Jeff
1983
$$L^2$$-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature. Zbl 1222.58013
Cheeger, Jeff; Dai, Xianzhe
2009
Remarks on the index theorem for families of Dirac operators on manifolds with boundary. Zbl 0727.58045
Bismut, Jean-Michel; Cheeger, Jeff
1991
$$L_p$$-bounds on curvature, elliptic estimates and rectifiability of singular sets. Zbl 1006.53034
Cheeger, Jeff
2002
Characterization of the Radon-Nikodym property in terms of inverse limits. Zbl 1191.46016
Cheeger, Jeff; Kleiner, Bruce
2008
Splittings and $$Cr$$-structures for manifolds with nonpositive sectional curvature. Zbl 1034.53038
Cao, Jianguo; Cheeger, Jeff; Rong, Xiaochun
2001
Invariants êta et indice des familles pour des variétés à bord. (Eta invariants and index of families for manifolds with boundary). Zbl 0645.58036
Bismut, Jean-Michel; Cheeger, Jeff
1987
A vanishing theorem for piecewise constant curvature spaces. Zbl 0612.53024
Cheeger, Jeff
1986
Local splitting structures on nonpositively curved manifolds and semirigidity in dimension 3. Zbl 1086.53050
Cao, Jianguo; Cheeger, Jeff; Rong, Xiaochun
2004
Structure theory and convergence in Riemannian geometry. Zbl 1205.53034
Cheeger, Jeff
2010
On the formulas of Atiyah-Patodi-Singer and Witten. Zbl 0676.58050
Cheeger, Jeff
1987
Metric and comparison geometry. Surveys in differential geometry. Vol. XI. Zbl 1149.53005
2007
Marcel Berger remembered. Zbl 1377.01033
Besson, Gérard; Gromov, Misha; Simons, James; Cheeger, Jeff; Bourguignon, Jean-Pierre; Sullivan, Dennis; Lafontaine, Jacques; Kazdan, Jerry; Michelsohn, Marie-Louise; Pansu, Pierre; Ebin, David; Grove, Karsten
2017
Rectifiability of singular sets of noncollapsed limit spaces with Ricci curvature bounded below. Zbl 1469.53083
Cheeger, Jeff; Jiang, Wenshuai; Naber, Aaron
2021
Marcel Berger remembered. Zbl 1377.01033
Besson, Gérard; Gromov, Misha; Simons, James; Cheeger, Jeff; Bourguignon, Jean-Pierre; Sullivan, Dennis; Lafontaine, Jacques; Kazdan, Jerry; Michelsohn, Marie-Louise; Pansu, Pierre; Ebin, David; Grove, Karsten
2017
Infinitesimal structure of differentiability spaces, and metric differentiation. Zbl 1360.30047
Cheeger, Jeff; Kleiner, Bruce; Schioppa, Andrea
2016
Regularity of Einstein manifolds and the codimension 4 conjecture. Zbl 1335.53057
Cheeger, Jeff; Naber, Aaron
2015
Critical sets of elliptic equations. Zbl 1309.35012
Cheeger, Jeff; Naber, Aaron; Valtorta, Daniele
2015
Inverse limit spaces satisfying a Poincaré inequality. Zbl 1331.46016
Cheeger, Jeff; Kleiner, Bruce
2015
Quantitative stratification and the regularity of harmonic map flow. Zbl 1317.53081
Cheeger, Jeff; Haslhofer, Robert; Naber, Aaron
2015
Lower bounds on Ricci curvature and quantitative behavior of singular sets. Zbl 1268.53053
Cheeger, Jeff; Naber, Aaron
2013
Quantitative stratification and the regularity of harmonic maps and minimal currents. Zbl 1269.53063
Cheeger, Jeff; Naber, Aaron
2013
Quantitative stratification and the regularity of mean curvature flow. Zbl 1277.53064
Cheeger, Jeff; Haslhofer, Robert; Naber, Aaron
2013
Realization of metric spaces as inverse limits, and bilipschitz embedding in $$L_1$$. Zbl 1277.46012
Cheeger, Jeff; Kleiner, Bruce
2013
Quantitative differentiation: a general formulation. Zbl 1258.30027
Cheeger, Jeff
2012
Compression bounds for Lipschitz maps from the Heisenberg group to $$L_{1}$$. Zbl 1247.46020
Cheeger, Jeff; Kleiner, Bruce; Naor, Assaf
2011
Differentiating maps into $$L^1$$, and the geometry of BV functions. Zbl 1194.22009
Cheeger, Jeff; Kleiner, Bruce
2010
Metric differentiation, monotonicity and maps to $$L^{1}$$. Zbl 1214.46013
Cheeger, Jeff; Kleiner, Bruce
2010
Structure theory and convergence in Riemannian geometry. Zbl 1205.53034
Cheeger, Jeff
2010
Differentiability of Lipschitz maps from metric measure spaces to Banach spaces with the Radon-Nikodym property. Zbl 1200.58007
Cheeger, Jeff; Kleiner, Bruce
2009
A $$(\log n)^{\Omega(1)}$$ integrality gap for the sparsest cut SDP. Zbl 1291.90318
Cheeger, Jeff; Kleiner, Bruce; Naor, Assaf
2009
$$L^2$$-cohomology of spaces with nonisolated conical singularities and nonmultiplicativity of the signature. Zbl 1222.58013
Cheeger, Jeff; Dai, Xianzhe
2009
Comparison theorems in Riemannian geometry. Reprint of the 1975 original. Zbl 1142.53003
Cheeger, Jeff; Ebin, David G.
2008
Characterization of the Radon-Nikodym property in terms of inverse limits. Zbl 1191.46016
Cheeger, Jeff; Kleiner, Bruce
2008
Metric and comparison geometry. Surveys in differential geometry. Vol. XI. Zbl 1149.53005
2007
On the differentiability of Lipschitz maps from metric measure spaces to Banach spaces. Zbl 1139.58004
Cheeger, Jeff; Kleiner, Bruce
2006
Curvature and injectivity radius estimates for Einstein 4-manifolds. Zbl 1092.53034
Cheeger, Jeff; Tian, Gang
2006
Generalized differentiation and bi-Lipschitz nonembedding in $$L^{1}$$. Zbl 1100.58004
Cheeger, Jeff; Kleiner, Bruce
2006
Anti-self-duality of curvature and degeneration of metrics with special holonomy. Zbl 1081.53038
Cheeger, Jeff; Tian, Gang
2005
Local splitting structures on nonpositively curved manifolds and semirigidity in dimension 3. Zbl 1086.53050
Cao, Jianguo; Cheeger, Jeff; Rong, Xiaochun
2004
Integral bounds on curvature, elliptic estimates and rectifiability of singular sets. Zbl 1086.53051
Cheeger, J.
2003
Degeneration of Einstein metrics and metrics with special holonomy. Zbl 1053.53028
Cheeger, Jeff
2003
On the singularities of spaces with bounded Ricci curvature. Zbl 1030.53046
Cheeger, J.; Colding, T. H.; Tian, G.
2002
$$L_p$$-bounds on curvature, elliptic estimates and rectifiability of singular sets. Zbl 1006.53034
Cheeger, Jeff
2002
Degeneration of Riemannian metrics under Ricci curvature bounds. Zbl 1055.53024
Cheeger, Jeff
2001
Splittings and $$Cr$$-structures for manifolds with nonpositive sectional curvature. Zbl 1034.53038
Cao, Jianguo; Cheeger, Jeff; Rong, Xiaochun
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
Differentiability of Lipschitz functions on metric measure spaces. Zbl 0942.58018
Cheeger, J.
1999
On the structure of spaces with Ricci curvature bounded below. I. Zbl 0902.53034
Cheeger, Jeff; Colding, Tobias H.
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
Existence of polarized $$F$$-structures on collapsed manifolds with bounded curvature and diameter. Zbl 0863.53026
Cheeger, J.; Rong, X.
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
Collapsed Riemannian manifolds with bounded diameter and bounded covering geometry. Zbl 0843.53039
Cheeger, J.; Rong, X.
1995
On the cone structure at infinity of Ricci flat manifolds with Euclidean volume growth and quadratic curvature decay. Zbl 0814.53034
Cheeger, Jeff; Tian, Gang
1994
Nilpotent structures and invariant metrics on collapsed manifolds. Zbl 0758.53022
Cheeger, Jeff; Fukaya, Kenji; Gromov, Mikhael
1992
$$C^ \alpha$$-compactness for manifolds with Ricci curvature and injectivity radius bounded below. Zbl 0774.53021
Anderson, Michael T.; Cheeger, Jeff
1992
Transgressed Euler classes of $$SL(2n,\mathbb{Z})$$ vector bundles, adiabatic limits of eta invariants and special values of $$L$$-functions. Zbl 0768.58048
Bismut, Jean-Michel; Cheeger, Jeff
1992
Critical points of distance functions and applications to geometry. Zbl 0771.53015
Cheeger, Jeff
1991
Diffeomorphism finiteness for manifolds with Ricci curvature and $$L^{n/2}$$-norm of curvature bounded. Zbl 0764.53026
Anderson, Michael T.; Cheeger, Jeff
1991
Chopping Riemannian manifolds. Zbl 0722.53045
Cheeger, Jeff; Gromov, Mikhael
1991
Remarks on the index theorem for families of Dirac operators on manifolds with boundary. Zbl 0727.58045
Bismut, Jean-Michel; Cheeger, Jeff
1991
Collapsing Riemannian manifolds while keeping their curvature bounded. II. Zbl 0727.53043
Cheeger, Jeff; Gromov, Mikhael
1990
Families index for manifolds with boundary, superconnections, and cones. I: Families of manifolds with boundary and Dirac operators. Zbl 0696.53021
Bismut, Jean-Michel; Cheeger, Jeff
1990
Families index for manifolds with boundary, superconnections and cones. II: The Chern character. Zbl 0711.53023
Bismut, Jean-Michel; Cheeger, Jeff
1990
$$\eta$$-invariants and their adiabatic limits. Zbl 0671.58037
Bismut, Jean-Michel; Cheeger, Jeff
1989
$$\eta$$-invariants, the adiabatic approximation and conical singularities. Zbl 0623.58021
Cheeger, Jeff
1987
Invariants êta et indice des familles pour des variétés à bord. (Eta invariants and index of families for manifolds with boundary). Zbl 0645.58036
Bismut, Jean-Michel; Cheeger, Jeff
1987
On the formulas of Atiyah-Patodi-Singer and Witten. Zbl 0676.58050
Cheeger, Jeff
1987
Collapsing Riemannian manifolds while keeping their curvature bounded. I. Zbl 0606.53028
Cheeger, Jeff; Gromov, Mikhael
1986
$$L_ 2$$-cohomology and group cohomology. Zbl 0597.57020
Cheeger, Jeff; Gromov, Mikhael
1986
Kinematic and tube formulas for piecewise linear spaces. Zbl 0615.53058
Cheeger, J.; Müller, W.; Schrader, R.
1986
A vanishing theorem for piecewise constant curvature spaces. Zbl 0612.53024
Cheeger, Jeff
1986
Differential characters and geometric invariants. Zbl 0621.57010
Cheeger, Jeff; Simons, James
1985
Bounds on the von Neumann dimension of $$L^ 2$$-cohomoloy and the Gauss- Bonnet theorem for open manifolds. Zbl 0614.53034
Cheeger, Jeff; Gromov, Mikhael
1985
On the characteristic numbers of complete manifolds of bounded curvature and finite volume. Zbl 0592.53036
Cheeger, Jeff; Gromov, Mikhael
1985
On the curvature of piecewise flat spaces. Zbl 0559.53028
Cheeger, Jeff; Müller, Werner; Schrader, Robert
1984
Spectral geometry of singular Riemannian spaces. Zbl 0529.58034
Cheeger, Jeff
1983
Hodge theory of complex cones. Zbl 0583.58004
Cheeger, Jeff
1983
Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. Zbl 0493.53035
Cheeger, Jeff; Gromov, Mikhail; Taylor, Michael
1982
On the diffraction of waves by conical singularities. I. Zbl 0526.58049
Cheeger, Jeff; Taylor, Michael
1982
$$L^ 2-$$cohomology and intersection homology of singular algebraic varieties. Zbl 0503.14008
Cheeger, Jeff; Goresky, Mark; MacPherson, Robert
1982
On the diffraction of waves by conical singularities. II. Zbl 0536.58032
Cheeger, Jeff; Taylor, Michael
1982
A lower bound for the heat kernel. Zbl 0481.35003
Cheeger, Jeff; Yau, Shing-Tung
1981
On the Hodge theory of Riemannian pseudomanifolds. Zbl 0461.58002
Cheeger, Jeff
1980
On the lower bound for the injectivity radius of 1/4-pinched Riemannian manifolds. Zbl 0468.53035
Cheeger, Jeff; Gromoll, Detlef
1980
Analytic torsion and the heat equation. Zbl 0412.58026
Cheeger, Jeff
1979
On the spectral geometry of spaces with cone-like singularities. Zbl 0411.58003
Cheeger, Jeff
1979
Analytic torsion and Reidemeister torsion. Zbl 0358.57005
Cheeger, Jeff
1977
Comparison theorems in Riemannian geometry. Zbl 0309.53035
Cheeger, Jeff; Ebin, David G.
1975
Some examples of manifolds of nonnegative curvature. Zbl 0281.53040
Cheeger, Jeff
1973
Multiplication of differential characters. Zbl 0285.53014
Cheeger, Jeff
1973
On the structure of complete manifolds of nonnegative curvature. Zbl 0246.53049
Cheeger, Jeff; Gromoll, Detlef
1972
The splitting theorem for manifolds of nonnegative Ricci curvature. Zbl 0223.53033
Cheeger, Jeff; Gromoll, Detlef
1971
A combinatorial formula for Stiefel-Whitney classes. Zbl 0282.57009
Cheeger, Jeff
1971
A lower bound for the smallest eigenvalue of the Laplacian. Zbl 0212.44903
Cheeger, J.
1970
Finiteness theorems for Riemannian manifolds. Zbl 0194.52902
Cheeger, J.
1970
Counting topological manifolds. Zbl 0199.58403
Cheeger, J.; Kister, J. M.
1970
Infinitesimal isometries and Pontryagin numbers. Zbl 0179.28802
Baum, P. F.; Cheeger, J.
1969
Pinching theorems for a certain class of Riemannian manifolds. Zbl 0183.50301
Cheeger, J.
1969
The relation between the Laplacian and the diameter for manifolds of non- negative curvature. Zbl 0177.50201
Cheeger, J.
1968
The structure of complete manifolds of nonnegative curvature. Zbl 0169.24101
Cheeger, J.; Gromoll, D.
1968
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### Cited by 2,944 Authors

 32 Cheeger, Jeff 32 Gigli, Nicola 26 Shanmugalingam, Nageswari 25 Wei, Guofang 24 Lott, John 22 Ambrosio, Luigi 22 Tian, Gang 21 Honda, Shouhei 20 Dai, Xianzhe 20 Naber, Aaron C. 19 Björn, Jana 17 Mondino, Andrea 17 Naor, Assaf 17 Rong, Xiaochun 17 Shiohama, Katsuhiro 17 Vertman, Boris 16 Donnelly, Harold 15 Björn, Anders 15 Kleiner, Bruce 15 Koskela, Pekka 14 Anderson, Michael T. 14 Taylor, Michael Eugene 13 Chen, Xiuxiong 13 Kapovitch, Vitali 13 Piazza, Paolo 12 Bismut, Jean-Michel 12 Grove, Karsten 12 Le Donne, Enrico 12 Pasqualetto, Enrico 12 Savaré, Giuseppe 12 Speight, Gareth 12 Wang, Bing 12 Xia, Changyu 12 Yamaguchi, Takao 12 Zhang, Weiping 11 Brüning, Jochen 11 Chow, Bennett 11 Colding, Tobias Holck 11 Galaz-Garcia, Fernando 11 Ludwig, Ursula Beate 11 Ma, Xiaonan 11 Mazzeo, Rafe R. 11 Pinamonti, Andrea 11 Rochon, Frédéric 11 Wilhelm, Frederick H. jun. 11 Yan, Lixin 10 Albin, Pierre 10 Bunke, Ulrich 10 Gromov, Mikhael Leonidovich 10 Guijarro, Luis 10 Innami, Nobuhiro 10 Kondo, Kei-Ichi 10 Petersen, Peter V 10 Saloff-Coste, Laurent 10 Shen, Zhongmin 10 Zhang, Zhenlei 9 Baudoin, Fabrice 9 Cao, Jianguo 9 Carron, Gilles 9 Jiang, Renjin 9 Li, Chi 9 Li, Hongquan 9 Li, Peter 9 Marola, Niko 9 Nagase, Masayoshi 9 Rajala, Tapio 9 Spreafico, Mauro 9 Tam, Luen-Fai 9 Tanaka, Minoru 9 Wang, Feng-Yu 9 Weinberger, Shmuel 9 Xu, Shicheng 9 Yau, Shing-Tung 9 Zhang, Huichun 8 Cochran, Thomas (Tim) Daniel 8 Eriksson-Bique, Sylvester 8 Eschenburg, Jost-Hinrich 8 Fang, Fuquan 8 Freed, Daniel Stuart 8 Greene, Robert Everist 8 Grigor’yan, Alexander Asaturovich 8 Han, Bangxian 8 Haslhofer, Robert 8 Itokawa, Yoe 8 Jiang, Wenshuai 8 Lu, Zhiqin 8 Mari, Luciano 8 Noronha, Maria Helena 8 Pan, Jiayin 8 Sauer, Roman 8 Schick, Thomas 8 Searle, Catherine 8 Shen, Shu 8 Sormani, Christina 8 Sun, Song 8 Tyson, Jeremy T. 8 Wang, Feng 8 Wang, Linfeng 8 Wang, Yusheng 8 Wu, Hung-Hsi ...and 2,844 more Authors
all top 5

### Cited in 398 Serials

 152 The Journal of Geometric Analysis 134 Journal of Functional Analysis 130 Proceedings of the American Mathematical Society 126 Transactions of the American Mathematical Society 109 Mathematische Zeitschrift 96 Advances in Mathematics 87 Inventiones Mathematicae 85 Duke Mathematical Journal 85 Annals of Global Analysis and Geometry 82 Mathematische Annalen 81 Communications in Mathematical Physics 77 Calculus of Variations and Partial Differential Equations 67 Differential Geometry and its Applications 64 Geometric and Functional Analysis. GAFA 56 Geometriae Dedicata 54 Journal of Geometry and Physics 54 Geometry & Topology 53 Annales de l’Institut Fourier 49 Manuscripta Mathematica 43 Journal für die Reine und Angewandte Mathematik 37 Journal of Mathematical Analysis and Applications 33 Potential Analysis 32 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 32 Tôhoku Mathematical Journal. Second Series 32 Journal de Mathématiques Pures et Appliquées. Neuvième Série 30 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 29 Comptes Rendus. Mathématique. Académie des Sciences, Paris 28 Revista Matemática Iberoamericana 28 Bulletin of the American Mathematical Society. New Series 27 Communications on Pure and Applied Mathematics 26 Israel Journal of Mathematics 24 Journal of Mathematical Physics 24 Acta Mathematica 23 Communications in Contemporary Mathematics 22 Journal of the American Mathematical Society 20 Analysis and Geometry in Metric Spaces 19 Archiv der Mathematik 19 Compositio Mathematica 19 Siberian Mathematical Journal 19 Communications in Partial Differential Equations 19 Science China. Mathematics 18 Journal d’Analyse Mathématique 18 International Journal of Mathematics 17 Journal of Differential Equations 16 Journal of the European Mathematical Society (JEMS) 16 Frontiers of Mathematics in China 15 Bulletin de la Société Mathématique de France 15 Annals of Mathematics. Second Series 15 Journal of High Energy Physics 15 Algebraic & Geometric Topology 13 Annali di Matematica Pura ed Applicata. Serie Quarta 13 Topology and its Applications 13 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 13 Analysis & PDE 13 Journal of Topology and Analysis 12 Annales Henri Poincaré 11 The Annals of Probability 11 Illinois Journal of Mathematics 11 Publications Mathématiques 11 Journal of the Mathematical Society of Japan 11 Kodai Mathematical Journal 11 Mathematische Nachrichten 11 Results in Mathematics 11 Chinese Annals of Mathematics. Series B 11 Probability Theory and Related Fields 11 Bulletin des Sciences Mathématiques 11 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 10 General Relativity and Gravitation 10 Nagoya Mathematical Journal 10 $$K$$-Theory 10 Journal of Mathematical Sciences (New York) 9 Letters in Mathematical Physics 9 Mathematical Notes 9 Commentarii Mathematici Helvetici 9 Memoirs of the American Mathematical Society 9 Discrete & Computational Geometry 8 Mathematical Proceedings of the Cambridge Philosophical Society 8 Monatshefte für Mathematik 8 Pacific Journal of Mathematics 8 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 8 Linear Algebra and its Applications 8 Acta Mathematica Sinica. English Series 8 Bulletin of the American Mathematical Society 8 Groups, Geometry, and Dynamics 8 Advances in Calculus of Variations 7 Wave Motion 7 Journal of Differential Geometry 7 Publications of the Research Institute for Mathematical Sciences, Kyoto University 7 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 7 St. Petersburg Mathematical Journal 7 Annales Academiae Scientiarum Fennicae. Mathematica 7 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 7 International Journal of Geometric Methods in Modern Physics 7 Journal of Noncommutative Geometry 7 Journal of Spectral Theory 7 Annales Fennici Mathematici 6 Discrete Mathematics 6 Bulletin of the London Mathematical Society 6 Proceedings of the Japan Academy. Series A 6 Annales Mathématiques Blaise Pascal ...and 298 more Serials
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### Cited in 61 Fields

 1,936 Differential geometry (53-XX) 1,031 Global analysis, analysis on manifolds (58-XX) 453 Partial differential equations (35-XX) 430 Manifolds and cell complexes (57-XX) 253 Functional analysis (46-XX) 204 Several complex variables and analytic spaces (32-XX) 173 Calculus of variations and optimal control; optimization (49-XX) 162 Functions of a complex variable (30-XX) 151 Potential theory (31-XX) 139 Probability theory and stochastic processes (60-XX) 127 Algebraic topology (55-XX) 124 Algebraic geometry (14-XX) 123 Quantum theory (81-XX) 113 Topological groups, Lie groups (22-XX) 104 Operator theory (47-XX) 101 Measure and integration (28-XX) 87 Relativity and gravitational theory (83-XX) 84 Group theory and generalizations (20-XX) 83 Combinatorics (05-XX) 77 Dynamical systems and ergodic theory (37-XX) 74 Convex and discrete geometry (52-XX) 69 Real functions (26-XX) 68 Harmonic analysis on Euclidean spaces (42-XX) 60 Abstract harmonic analysis (43-XX) 59 $$K$$-theory (19-XX) 49 Geometry (51-XX) 48 General topology (54-XX) 40 Number theory (11-XX) 37 Numerical analysis (65-XX) 34 Computer science (68-XX) 28 Operations research, mathematical programming (90-XX) 26 Ordinary differential equations (34-XX) 26 Statistics (62-XX) 21 Statistical mechanics, structure of matter (82-XX) 15 Mechanics of particles and systems (70-XX) 15 Mechanics of deformable solids (74-XX) 15 Fluid mechanics (76-XX) 13 Information and communication theory, circuits (94-XX) 12 Special functions (33-XX) 11 Linear and multilinear algebra; matrix theory (15-XX) 11 Approximations and expansions (41-XX) 11 Systems theory; control (93-XX) 10 Category theory; homological algebra (18-XX) 10 Optics, electromagnetic theory (78-XX) 9 Mathematical logic and foundations (03-XX) 9 Commutative algebra (13-XX) 9 Nonassociative rings and algebras (17-XX) 7 General and overarching topics; collections (00-XX) 7 Difference and functional equations (39-XX) 6 History and biography (01-XX) 6 Integral transforms, operational calculus (44-XX) 6 Classical thermodynamics, heat transfer (80-XX) 5 Associative rings and algebras (16-XX) 5 Biology and other natural sciences (92-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 Integral equations (45-XX) 2 Astronomy and astrophysics (85-XX) 1 General algebraic systems (08-XX) 1 Field theory and polynomials (12-XX) 1 Mathematics education (97-XX)

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