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Petersen, Peter V

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Author ID: petersen.peter-v Recent zbMATH articles by "Petersen, Peter V"
Published as: Petersen, Peter; Petersen, Peter V; Petersen, P.
Homepage: http://www.math.ucla.edu/~petersen/
External Links: MGP
Documents Indexed: 64 Publications since 1988, including 6 Books

Publications by Year

Citations contained in zbMATH Open

53 Publications have been cited 1,162 times in 860 Documents Cited by Year
Riemannian geometry. 2nd ed. Zbl 1220.53002
Petersen, Peter
212
2006
Riemannian geometry. Zbl 0914.53001
Petersen, Peter
116
1998
Rigidity of gradient Ricci solitons. Zbl 1176.53048
Petersen, Peter; Wylie, William
81
2009
On the classification of gradient Ricci solitons. Zbl 1202.53049
Petersen, Peter; Wylie, William
60
2010
Relative volume comparison with integral curvature bounds. Zbl 0910.53029
Petersen, P.; Wei, G.
59
1997
On gradient Ricci solitons with symmetry. Zbl 1168.53021
Petersen, Peter; Wylie, William
56
2009
Bounding homotopy types by geometry. Zbl 0655.53032
Grove, Karsten; Petersen, Peter V
45
1988
On the classification of warped product Einstein metrics. Zbl 1270.53075
He, Chenxu; Petersen, Peter; Wylie, William
40
2012
Manifolds near the boundary of existence. Zbl 0729.53045
Grove, Karsten; Petersen, Peter V
39
1991
Geometric finiteness theorems via controlled topology. Zbl 0747.53033
Grove, Karsten; Petersen, Peter V; Wu, Jyh-Yang
38
1990
Riemannian geometry. 3rd edition. Zbl 1417.53001
Petersen, Peter
38
2016
Analysis and geometry on manifolds with integral Ricci curvature bounds. II. Zbl 0999.53030
Petersen, Peter; Wei, Guofang
28
2001
Integral curvature bounds, distance estimates and applications. Zbl 0969.53017
Petersen, Peter; Sprouse, Chadwick
26
1998
Convergence theorems in Riemannian geometry. Zbl 0898.53035
Petersen, Peter
25
1997
A radius sphere theorem. Zbl 0801.53029
Grove, Karsten; Petersen, Peter
23
1993
A finiteness theorem for metric spaces. Zbl 0696.55005
Petersen, Peter
21
1990
A pinching theorem for homotopy spheres. Zbl 0717.53025
Grove, Karsten; Petersen, Peter V
21
1990
Examples of Riemannian manifolds with positive curvature almost everywhere. Zbl 0963.53020
Petersen, Peter; Wilhelm, Frederick
16
1999
Gromov-Hausdorff convergence of metric spaces. Zbl 0788.53037
Petersen, Peter V
15
1993
Little topology, big volume. Zbl 0772.53033
Greene, Robert E.; Petersen, Peter V
14
1992
Erratum: Geometric finiteness theorems via controlled topology. Zbl 0778.53034
Grove, Karsten; Petersen, Peter V; Wu, Jyh-Yang
13
1991
On eigenvalue pinching in positive Ricci curvature. Zbl 0988.53011
Petersen, Peter
13
1999
Classification of almost quarter-pinched manifolds. Zbl 1168.53020
Petersen, Peter; Tao, Terence
13
2009
Compactness and finiteness theorems for isospectral manifolds. Zbl 0737.53038
Brooks, Robert; Perry, Peter; Petersen, Peter V
12
1992
Controlled geometry via smoothing. Zbl 0994.53019
Petersen, Peter; Wei, Guofang; Ye, Rugang
10
1999
Riemannian manifolds of faster-than-quadratic curvature decay. Zbl 0833.53037
Green, Robert E.; Petersen, Peter; Zhu, Shunhui
10
1994
Volume comparison à la Aleksandrov. Zbl 0758.53035
Grove, Karsten; Petersen, Peter V
10
1992
Warped product rigidity. Zbl 1316.53044
He, Chenxu; Petersen, Peter; Wylie, William
9
2015
Small excess and Ricci curvature. Zbl 0742.53013
Petersen, Peter
8
1991
Integral pinching theorems. Zbl 0970.53022
Dai, Xianzhe; Petersen, Peter; Wei, Guofang
7
2000
On Cheeger’s inequality. Zbl 0809.53049
Brooks, Robert; Perry, Peter; Petersen, Peter V
7
1993
Warped product Einstein metrics on homogeneous spaces and homogeneous Ricci solitons. Zbl 1328.53053
He, Chenxu; Petersen, Peter; Wylie, William
7
2015
A step towards the Alekseevskii conjecture. Zbl 1367.53041
Jablonski, Michael; Petersen, Peter
7
2017
Comparison geometry with integral curvature bounds. Zbl 0910.53030
Petersen, P.; Shteingold, S. D.; Wei, G.
6
1997
Aspects of global Riemannian geometry. Zbl 0961.53019
Petersen, Peter
6
1999
Homotopy types of positively curved manifolds with large volume. Zbl 0662.53034
Grove, Karsten; Petersen, Peter V
6
1988
An excess sphere theorem. Zbl 0771.53024
Petersen, Peter V; Zhu, Shunhui
5
1993
Spaces on and beyond the boundary of existence. Zbl 0839.53032
Petersen, Peter; Wilhelm, Frederick; Zhu, Shun-hui
5
1995
On Frankel’s theorem. Zbl 1035.53080
Petersen, Peter; Wilhelm, Frederick
5
2003
Warped product Einstein metrics over spaces with constant scalar curvature. Zbl 1292.53030
He, Chenxu; Petersen, Peter; Wylie, William
4
2014
Comparison geometry problem list. Zbl 0843.53031
Petersen, Peter
3
1996
Manifolds with small excess and bounded curvature. Zbl 0791.53047
Petersen, Peter V; Shen, Zhongmin; Zhu, Shunhui
3
1993
Comparison geometry. Zbl 0871.00023
Grove, Karsten (ed.); Petersen, Peter (ed.)
3
1997
Rigidity in non-negative curvature. Zbl 1008.53042
Guijarro, Luis; Petersen, Peter
3
1997
Uniqueness of warped product Einstein metrics and applications. Zbl 1335.53019
He, Chenxu; Petersen, Peter; Wylie, William
3
2015
Generalized doubling meets Poincaré. Zbl 1143.46015
Hinde, Colin; Petersen, Peter
2
2007
Fatness of covers. Zbl 0675.57001
Petersen, Peter V
2
1989
Linear stability of algebraic Ricci solitons. Zbl 1337.53055
Jablonski, Michael; Petersen, Peter; Williams, Michael Bradford
2
2016
\(U(2)\) invariant four dimensional Einstein metrics. Zbl 0869.53030
Petersen, Peter; Zhu, Shunhui
1
1995
Observer fields and the strong energy condition. Zbl 0861.53065
Petersen, Peter; Walschap, Gerard
1
1996
Eigenvalue pitching on \(p\)-forms. Zbl 1065.53035
Petersen, Peter; Sprouse, Chadwick
1
2001
Groups, coverings and Galois theory. Zbl 0749.57001
Hansen, Vagn Lundsgaard; Petersen, Peter V
1
1991
Eigenvalue pinching for Riemannian vector bundles. Zbl 0944.58024
Petersen, Peter; Sprouse, Chadwick
1
1999
A step towards the Alekseevskii conjecture. Zbl 1367.53041
Jablonski, Michael; Petersen, Peter
7
2017
Riemannian geometry. 3rd edition. Zbl 1417.53001
Petersen, Peter
38
2016
Linear stability of algebraic Ricci solitons. Zbl 1337.53055
Jablonski, Michael; Petersen, Peter; Williams, Michael Bradford
2
2016
Warped product rigidity. Zbl 1316.53044
He, Chenxu; Petersen, Peter; Wylie, William
9
2015
Warped product Einstein metrics on homogeneous spaces and homogeneous Ricci solitons. Zbl 1328.53053
He, Chenxu; Petersen, Peter; Wylie, William
7
2015
Uniqueness of warped product Einstein metrics and applications. Zbl 1335.53019
He, Chenxu; Petersen, Peter; Wylie, William
3
2015
Warped product Einstein metrics over spaces with constant scalar curvature. Zbl 1292.53030
He, Chenxu; Petersen, Peter; Wylie, William
4
2014
On the classification of warped product Einstein metrics. Zbl 1270.53075
He, Chenxu; Petersen, Peter; Wylie, William
40
2012
On the classification of gradient Ricci solitons. Zbl 1202.53049
Petersen, Peter; Wylie, William
60
2010
Rigidity of gradient Ricci solitons. Zbl 1176.53048
Petersen, Peter; Wylie, William
81
2009
On gradient Ricci solitons with symmetry. Zbl 1168.53021
Petersen, Peter; Wylie, William
56
2009
Classification of almost quarter-pinched manifolds. Zbl 1168.53020
Petersen, Peter; Tao, Terence
13
2009
Generalized doubling meets Poincaré. Zbl 1143.46015
Hinde, Colin; Petersen, Peter
2
2007
Riemannian geometry. 2nd ed. Zbl 1220.53002
Petersen, Peter
212
2006
On Frankel’s theorem. Zbl 1035.53080
Petersen, Peter; Wilhelm, Frederick
5
2003
Analysis and geometry on manifolds with integral Ricci curvature bounds. II. Zbl 0999.53030
Petersen, Peter; Wei, Guofang
28
2001
Eigenvalue pitching on \(p\)-forms. Zbl 1065.53035
Petersen, Peter; Sprouse, Chadwick
1
2001
Integral pinching theorems. Zbl 0970.53022
Dai, Xianzhe; Petersen, Peter; Wei, Guofang
7
2000
Examples of Riemannian manifolds with positive curvature almost everywhere. Zbl 0963.53020
Petersen, Peter; Wilhelm, Frederick
16
1999
On eigenvalue pinching in positive Ricci curvature. Zbl 0988.53011
Petersen, Peter
13
1999
Controlled geometry via smoothing. Zbl 0994.53019
Petersen, Peter; Wei, Guofang; Ye, Rugang
10
1999
Aspects of global Riemannian geometry. Zbl 0961.53019
Petersen, Peter
6
1999
Eigenvalue pinching for Riemannian vector bundles. Zbl 0944.58024
Petersen, Peter; Sprouse, Chadwick
1
1999
Riemannian geometry. Zbl 0914.53001
Petersen, Peter
116
1998
Integral curvature bounds, distance estimates and applications. Zbl 0969.53017
Petersen, Peter; Sprouse, Chadwick
26
1998
Relative volume comparison with integral curvature bounds. Zbl 0910.53029
Petersen, P.; Wei, G.
59
1997
Convergence theorems in Riemannian geometry. Zbl 0898.53035
Petersen, Peter
25
1997
Comparison geometry with integral curvature bounds. Zbl 0910.53030
Petersen, P.; Shteingold, S. D.; Wei, G.
6
1997
Comparison geometry. Zbl 0871.00023
Grove, Karsten; Petersen, Peter
3
1997
Rigidity in non-negative curvature. Zbl 1008.53042
Guijarro, Luis; Petersen, Peter
3
1997
Comparison geometry problem list. Zbl 0843.53031
Petersen, Peter
3
1996
Observer fields and the strong energy condition. Zbl 0861.53065
Petersen, Peter; Walschap, Gerard
1
1996
Spaces on and beyond the boundary of existence. Zbl 0839.53032
Petersen, Peter; Wilhelm, Frederick; Zhu, Shun-hui
5
1995
\(U(2)\) invariant four dimensional Einstein metrics. Zbl 0869.53030
Petersen, Peter; Zhu, Shunhui
1
1995
Riemannian manifolds of faster-than-quadratic curvature decay. Zbl 0833.53037
Green, Robert E.; Petersen, Peter; Zhu, Shunhui
10
1994
A radius sphere theorem. Zbl 0801.53029
Grove, Karsten; Petersen, Peter
23
1993
Gromov-Hausdorff convergence of metric spaces. Zbl 0788.53037
Petersen, Peter V
15
1993
On Cheeger’s inequality. Zbl 0809.53049
Brooks, Robert; Perry, Peter; Petersen, Peter V
7
1993
An excess sphere theorem. Zbl 0771.53024
Petersen, Peter V; Zhu, Shunhui
5
1993
Manifolds with small excess and bounded curvature. Zbl 0791.53047
Petersen, Peter V; Shen, Zhongmin; Zhu, Shunhui
3
1993
Little topology, big volume. Zbl 0772.53033
Greene, Robert E.; Petersen, Peter V
14
1992
Compactness and finiteness theorems for isospectral manifolds. Zbl 0737.53038
Brooks, Robert; Perry, Peter; Petersen, Peter V
12
1992
Volume comparison à la Aleksandrov. Zbl 0758.53035
Grove, Karsten; Petersen, Peter V
10
1992
Manifolds near the boundary of existence. Zbl 0729.53045
Grove, Karsten; Petersen, Peter V
39
1991
Erratum: Geometric finiteness theorems via controlled topology. Zbl 0778.53034
Grove, Karsten; Petersen, Peter V; Wu, Jyh-Yang
13
1991
Small excess and Ricci curvature. Zbl 0742.53013
Petersen, Peter
8
1991
Groups, coverings and Galois theory. Zbl 0749.57001
Hansen, Vagn Lundsgaard; Petersen, Peter V
1
1991
Geometric finiteness theorems via controlled topology. Zbl 0747.53033
Grove, Karsten; Petersen, Peter V; Wu, Jyh-Yang
38
1990
A finiteness theorem for metric spaces. Zbl 0696.55005
Petersen, Peter
21
1990
A pinching theorem for homotopy spheres. Zbl 0717.53025
Grove, Karsten; Petersen, Peter V
21
1990
Fatness of covers. Zbl 0675.57001
Petersen, Peter V
2
1989
Bounding homotopy types by geometry. Zbl 0655.53032
Grove, Karsten; Petersen, Peter V
45
1988
Homotopy types of positively curved manifolds with large volume. Zbl 0662.53034
Grove, Karsten; Petersen, Peter V
6
1988
all top 5

Cited by 912 Authors

21 Petersen, Peter V
13 Paeng, Seong-Hun
13 Wei, Guofang
12 Ribeiro, Ernani jun.
11 García-Río, Eduardo
10 Catino, Giovanni
10 Grove, Karsten
10 Rong, Xiaochun
10 Stepanov, Sergeĭ Evgen’evich
9 Sormani, Christina
9 Wilhelm, Frederick H. jun.
8 Wu, Jiayong
8 Wylie, William C.
8 Xu, Hongwei
7 DeVito, Jason
7 Fernández-López, Manuel
7 Rigoli, Marco
7 Tsyganok, Irina Ivanovna
7 Wang, Peihe
7 Yamaguchi, Takao
6 Barros, Abdênago A.
6 Cho, Jong Taek
6 Guijarro, Luis
6 Mastrolia, Paolo
6 Naber, Aaron C.
6 Pigola, Stefano
6 Rimoldi, Michele
6 Shen, Zhongmin
5 Allen, Brian Michael
5 Anderson, Michael T.
5 Crâşmăreanu, Mircea
5 Gu, Juan-Ru
5 Kapovitch, Vitali
5 Lafuente, Ramiro A.
5 Lassas, Matti
5 Mao, Jing
5 Rubinstein, Yanir A.
5 Tian, Gang
5 Vîlcu, Costin
5 Wang, Bing
5 Wang, Linfeng
5 Wu, Bingye
5 Xu, Shicheng
5 Zhu, Meng
4 Berchio, Elvise
4 Calvaruso, Giovanni
4 Carfora, Mauro
4 Case, Jeffrey S.
4 Chen, Xiaoyang
4 Dai, Xianzhe
4 Jiang, Wenshuai
4 Katsuda, Atsushi
4 Ma, Li
4 Mazzieri, Lorenzo
4 Mikeš, Josef
4 Mitsuishi, Ayato
4 Plaut, Conrad P.
4 Searle, Catherine
4 Setti, Alberto G.
4 Shioya, Takashi
4 Silva Filho, João F.
4 Tadano, Homare
4 Tanaka, Minoru
4 Walsh, Mark G.
4 Wraith, David J.
4 Wu, Peng
4 Zhu, Shunhui
3 Akutagawa, Kazuo
3 Alexandrino, Marcos M.
3 Ambrosio, Luigi
3 Bamler, Richard H.
3 Barretta, Raffaele
3 Belegradek, Igor
3 Bercu, Gabriel
3 Besson, Gérard
3 Bohm, Christoph
3 Brooks, Robert Wolfe
3 Cabezas-Rivas, Esther
3 Calviño-Louzao, Esteban
3 Carron, Gilles
3 Cheeger, Jeff
3 Chen, Zhiqi
3 Chow, Bennett
3 Cui, Xiaojun
3 De, Uday Chand
3 Deng, Li
3 Ding, Qing
3 Diógenes, Rafael
3 Galaz-Garcia, Fernando
3 Ganguly, Debdip
3 Gimeno, Vicent
3 Gomes, José Nazareno Vieira
3 Grillo, Gabriele
3 Guo, Hongxin
3 Harvey, John Matthew
3 Honda, Shouhei
3 Ketterer, Christian
3 Khuri, Marcus A.
3 Kimura, Makoto
3 Kurylev, Yaroslav V.
...and 812 more Authors
all top 5

Cited in 191 Serials

58 The Journal of Geometric Analysis
50 Differential Geometry and its Applications
48 Proceedings of the American Mathematical Society
35 Annals of Global Analysis and Geometry
30 Mathematische Zeitschrift
29 Journal of Geometry and Physics
28 Transactions of the American Mathematical Society
24 Advances in Mathematics
24 Calculus of Variations and Partial Differential Equations
23 Journal of Mathematical Analysis and Applications
22 Geometriae Dedicata
21 Mathematische Annalen
13 Geometric and Functional Analysis. GAFA
12 Inventiones Mathematicae
11 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods
10 Duke Mathematical Journal
10 Journal of Functional Analysis
10 Geometry & Topology
10 International Journal of Geometric Methods in Modern Physics
9 Communications in Mathematical Physics
9 General Relativity and Gravitation
9 Results in Mathematics
8 Science China. Mathematics
7 Acta Mathematica
7 Annales de l’Institut Fourier
7 Pacific Journal of Mathematics
7 Journal de Mathématiques Pures et Appliquées. Neuvième Série
7 Bulletin of the American Mathematical Society. New Series
7 Advances in Geometry
7 Frontiers of Mathematics in China
6 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série
6 Archiv der Mathematik
6 Journal für die Reine und Angewandte Mathematik
6 International Journal of Mathematics
6 Communications in Contemporary Mathematics
6 Comptes Rendus. Mathématique. Académie des Sciences, Paris
6 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
5 Manuscripta Mathematica
5 Tohoku Mathematical Journal. Second Series
5 Revista Matemática Iberoamericana
5 Journal of the American Mathematical Society
5 Communications in Partial Differential Equations
5 Annals of Mathematics. Second Series
5 Bulletin of the Brazilian Mathematical Society. New Series
4 Journal of Mathematical Physics
4 Annali di Matematica Pura ed Applicata. Serie Quarta
4 Journal of Differential Equations
4 Journal of Geometry
4 Topology and its Applications
4 Chinese Annals of Mathematics. Series B
4 Journal of the European Mathematical Society (JEMS)
4 International Electronic Journal of Geometry
3 Mathematical Notes
3 Compositio Mathematica
3 Glasgow Mathematical Journal
3 Illinois Journal of Mathematics
3 International Journal of Mathematics and Mathematical Sciences
3 Journal of the Mathematical Society of Japan
3 Memoirs of the American Mathematical Society
3 Acta Mathematica Hungarica
3 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire
3 Journal of Mathematical Sciences (New York)
3 St. Petersburg Mathematical Journal
3 Discrete and Continuous Dynamical Systems
3 Mediterranean Journal of Mathematics
3 Journal of Topology and Analysis
3 Advances in Mathematical Physics
2 Acta Mechanica
2 Communications on Pure and Applied Mathematics
2 Discrete Mathematics
2 Letters in Mathematical Physics
2 Mathematical Proceedings of the Cambridge Philosophical Society
2 Physics Letters. B
2 Annales Polonici Mathematici
2 Journal of the Korean Mathematical Society
2 Monatshefte für Mathematik
2 Siberian Mathematical Journal
2 Bulletin of the Iranian Mathematical Society
2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
2 Russian Mathematics
2 Selecta Mathematica. New Series
2 Transformation Groups
2 Acta Mathematica Sinica. English Series
2 Living Reviews in Relativity
2 Annales Henri Poincaré
2 Algebraic & Geometric Topology
2 Foundations of Computational Mathematics
2 Milan Journal of Mathematics
2 Communications in Mathematics
2 Analysis and Geometry in Metric Spaces
2 Journal de l’École Polytechnique – Mathématiques
2 Korean Journal of Mathematics
1 Applicable Analysis
1 Israel Journal of Mathematics
1 Nuclear Physics. B
1 Rocky Mountain Journal of Mathematics
1 ZAMP. Zeitschrift für angewandte Mathematik und Physik
1 Arkiv för Matematik
1 Mathematics of Computation
1 Bulletin of Mathematical Biology
...and 91 more Serials
all top 5

Cited in 54 Fields

731 Differential geometry (53-XX)
160 Global analysis, analysis on manifolds (58-XX)
110 Partial differential equations (35-XX)
73 Manifolds and cell complexes (57-XX)
35 Relativity and gravitational theory (83-XX)
30 Calculus of variations and optimal control; optimization (49-XX)
18 Several complex variables and analytic spaces (32-XX)
17 Topological groups, Lie groups (22-XX)
16 Algebraic topology (55-XX)
14 Quantum theory (81-XX)
13 Geometry (51-XX)
12 Convex and discrete geometry (52-XX)
12 General topology (54-XX)
11 Probability theory and stochastic processes (60-XX)
10 Algebraic geometry (14-XX)
10 Potential theory (31-XX)
10 Mechanics of deformable solids (74-XX)
9 Dynamical systems and ergodic theory (37-XX)
8 Functional analysis (46-XX)
8 Statistics (62-XX)
8 Mechanics of particles and systems (70-XX)
8 Fluid mechanics (76-XX)
7 Combinatorics (05-XX)
7 Functions of a complex variable (30-XX)
7 Operator theory (47-XX)
6 Nonassociative rings and algebras (17-XX)
6 Real functions (26-XX)
5 Measure and integration (28-XX)
5 Numerical analysis (65-XX)
5 Computer science (68-XX)
4 Group theory and generalizations (20-XX)
4 Operations research, mathematical programming (90-XX)
3 Ordinary differential equations (34-XX)
3 Harmonic analysis on Euclidean spaces (42-XX)
3 Biology and other natural sciences (92-XX)
3 Systems theory; control (93-XX)
2 History and biography (01-XX)
2 Mathematical logic and foundations (03-XX)
2 Approximations and expansions (41-XX)
2 Optics, electromagnetic theory (78-XX)
2 Information and communication theory, circuits (94-XX)
1 General and overarching topics; collections (00-XX)
1 Number theory (11-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Associative rings and algebras (16-XX)
1 \(K\)-theory (19-XX)
1 Difference and functional equations (39-XX)
1 Abstract harmonic analysis (43-XX)
1 Integral transforms, operational calculus (44-XX)
1 Integral equations (45-XX)
1 Classical thermodynamics, heat transfer (80-XX)
1 Astronomy and astrophysics (85-XX)
1 Geophysics (86-XX)
1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

Citations by Year