# zbMATH — the first resource for mathematics

## Cao, Jianguo

Compute Distance To:
 Author ID: cao.jianguo Published as: Cao, J.; Cao, J.-G.; Cao, Jianguo Homepage: http://math.nd.edu/people/faculty/jianguo-cao/ External Links: MGP
 Documents Indexed: 32 Publications since 1984
all top 5

#### Co-Authors

 7 single-authored 4 Shaw, Mei-Chi 2 Benjamini, Itai 2 Chang, Shu-Cheng 2 Cheeger, Jeff 2 Dai, Bo 2 DeTurck, Dennis M. 2 Mei, Jiaqiang 2 Rong, Xiaochun 2 Tang, Hongyan 1 Calabi, Eugenio 1 Chen, Xiaoyang 1 Escobar, José Fernando 1 Fan, Huijun 1 Ge, Jian 1 Ledrappier, François 1 Wang, Lihe 1 Xavier, Frederico V.
all top 5

#### Serials

 3 Communications in Contemporary Mathematics 2 Mathematische Zeitschrift 2 Transactions of the American Mathematical Society 2 Communications in Analysis and Geometry 2 Frontiers of Mathematics in China 1 American Journal of Mathematics 1 Duke Mathematical Journal 1 Hokkaido Mathematical Journal 1 Indiana University Mathematics Journal 1 Inventiones Mathematicae 1 Journal of Differential Geometry 1 Mathematische Annalen 1 Michigan Mathematical Journal 1 Journal of Nanjing University. Natural Sciences 1 Ergodic Theory and Dynamical Systems 1 Advances in Mathematics 1 Differential Geometry and its Applications 1 The Journal of Geometric Analysis
all top 5

#### Fields

 22 Differential geometry (53-XX) 5 Several complex variables and analytic spaces (32-XX) 5 Global analysis, analysis on manifolds (58-XX) 3 Manifolds and cell complexes (57-XX) 2 Functions of a complex variable (30-XX) 2 Partial differential equations (35-XX) 2 Probability theory and stochastic processes (60-XX) 1 Algebraic geometry (14-XX) 1 Calculus of variations and optimal control; optimization (49-XX)

#### Citations contained in zbMATH Open

27 Publications have been cited 190 times in 164 Documents Cited by Year
Estimates for the $$\bar\partial$$-Neumann problem and nonexistence of $$C^2$$ Levi-flat hypersurfaces in $$\mathbb{C} P^n$$. Zbl 1057.32012
Cao, Jianguo; Shaw, Mei-Chi; Wang, Lihe
2004
The existence of generalized isothermal coordinates for higher dimensional Riemannian manifolds. Zbl 0715.53016
Cao, Jianguo
1991
Simple closed geodesics on convex surfaces. Zbl 0768.53019
Calabi, Eugenio; Cao, Jianguo
1992
Finsler geometry of projectivized vector bundles. Zbl 1086.53092
Cao, J.-G.; Wong, Pit-Mann
2003
The $$\bar\partial$$-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in $$\mathbb{C}P^n$$ with $$n \geq 3$$. Zbl 1124.32017
Cao, Jianguo; Shaw, Mei-Chi
2007
A new isoperimetric comparison theorem for surfaces of variable curvature. Zbl 0886.53031
Benjamini, Itai; Cao, Jianguo
1996
Pseudo-Einstein and $$Q$$-flat metrics with eigenvalue estimates on CR-hypersurfaces. Zbl 1155.32024
Cao, Jianguo; Chang, Shu-Cheng
2007
The Ricci curvature equation with rotational symmetry. Zbl 0824.53034
Cao, Jianguo; DeTurck, Dennis
1994
Kähler parabolicity and the Euler number of compact manifolds of non-positive sectional curvature. Zbl 0992.53031
Cao, Jianguo; Xavier, Frederico
2001
Cheeger isoperimetric constants of Gromov-hyperbolic spaces with quasi-poles. Zbl 0981.53021
Cao, Jianguo
2000
A simple proof of Perelman’s collapsing theorem for 3-manifolds. Zbl 1246.53052
Cao, Jianguo; Ge, Jian
2011
A new proof of the Takeuchi theorem. Zbl 1108.32013
Cao, Jianguo; Shaw, Meichi
2005
An optimal extension of Perelman’s comparison theorem for quadrangles and its applications. Zbl 1201.53040
Cao, Jianguo; Dai, Bo; Mei, Jiaqiang
2010
Splittings and $$Cr$$-structures for manifolds with nonpositive sectional curvature. Zbl 1034.53038
Cao, Jianguo; Cheeger, Jeff; Rong, Xiaochun
2001
Examples of simply-connected Liouville manifolds with positive spectrum. Zbl 0861.53033
Benjamini, Itai; Cao, Jianguo
1996
Prescribing Ricci curvature on open surfaces. Zbl 0751.53014
Cao, Jianguo; DeTurck, Dennis
1991
Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus. Zbl 1374.14007
Binda, F.; Cao, J.; Kai, W.; Sugiyama, R.
2017
Local splitting structures on nonpositively curved manifolds and semirigidity in dimension 3. Zbl 1086.53050
Cao, Jianguo; Cheeger, Jeff; Rong, Xiaochun
2004
Certain 4-manifolds with non-negative sectional curvature. Zbl 1167.53035
Cao, Jianguo
2008
An intrinsic proof of Gromoll – Grove diameter rigidity theorem. Zbl 1151.53027
Cao, Jianguo; Tang, Hongyan
2007
The Bers-Nielsen kernels and souls of open surfaces with negatice curvature. Zbl 0799.30032
Cao, Jianguo
1994
Minimal volume and simplicial volume of visibility $$n$$-manifolds and all 3-manifolds. Zbl 1320.53047
Cao, Jianguo; Chen, Xiaoyang
2012
A quadrangle comparison theorem and its application to soul theory for Alexandrov spaces. Zbl 1219.53036
Cao, Jianguo; Dai, Bo; Mei, Jiaqiang
2011
The modified Calabi-Yau problems for CR-manifolds. Zbl 1170.53052
Cao, Jianguo; Chang, Shu-Cheng
2008
Martin points on open manifolds of non-positive curvature. Zbl 1132.58016
Cao, Jianguo; Fan, Huijun; Ledrappier, François
2007
The smoothness of Riemannian submersions with non-negative sectional curvature. Zbl 1070.53014
Cao, Jianguo; Shaw, Mei-Chi
2005
Rigidity for non-compact surfaces of finite area and certain Kähler manifolds. Zbl 0845.57011
Cao, Jianguo
1995
Torsion and divisibility for reciprocity sheaves and 0-cycles with modulus. Zbl 1374.14007
Binda, F.; Cao, J.; Kai, W.; Sugiyama, R.
2017
Minimal volume and simplicial volume of visibility $$n$$-manifolds and all 3-manifolds. Zbl 1320.53047
Cao, Jianguo; Chen, Xiaoyang
2012
A simple proof of Perelman’s collapsing theorem for 3-manifolds. Zbl 1246.53052
Cao, Jianguo; Ge, Jian
2011
A quadrangle comparison theorem and its application to soul theory for Alexandrov spaces. Zbl 1219.53036
Cao, Jianguo; Dai, Bo; Mei, Jiaqiang
2011
An optimal extension of Perelman’s comparison theorem for quadrangles and its applications. Zbl 1201.53040
Cao, Jianguo; Dai, Bo; Mei, Jiaqiang
2010
Certain 4-manifolds with non-negative sectional curvature. Zbl 1167.53035
Cao, Jianguo
2008
The modified Calabi-Yau problems for CR-manifolds. Zbl 1170.53052
Cao, Jianguo; Chang, Shu-Cheng
2008
The $$\bar\partial$$-Cauchy problem and nonexistence of Lipschitz Levi-flat hypersurfaces in $$\mathbb{C}P^n$$ with $$n \geq 3$$. Zbl 1124.32017
Cao, Jianguo; Shaw, Mei-Chi
2007
Pseudo-Einstein and $$Q$$-flat metrics with eigenvalue estimates on CR-hypersurfaces. Zbl 1155.32024
Cao, Jianguo; Chang, Shu-Cheng
2007
An intrinsic proof of Gromoll – Grove diameter rigidity theorem. Zbl 1151.53027
Cao, Jianguo; Tang, Hongyan
2007
Martin points on open manifolds of non-positive curvature. Zbl 1132.58016
Cao, Jianguo; Fan, Huijun; Ledrappier, François
2007
A new proof of the Takeuchi theorem. Zbl 1108.32013
Cao, Jianguo; Shaw, Meichi
2005
The smoothness of Riemannian submersions with non-negative sectional curvature. Zbl 1070.53014
Cao, Jianguo; Shaw, Mei-Chi
2005
Estimates for the $$\bar\partial$$-Neumann problem and nonexistence of $$C^2$$ Levi-flat hypersurfaces in $$\mathbb{C} P^n$$. Zbl 1057.32012
Cao, Jianguo; Shaw, Mei-Chi; Wang, Lihe
2004
Local splitting structures on nonpositively curved manifolds and semirigidity in dimension 3. Zbl 1086.53050
Cao, Jianguo; Cheeger, Jeff; Rong, Xiaochun
2004
Finsler geometry of projectivized vector bundles. Zbl 1086.53092
Cao, J.-G.; Wong, Pit-Mann
2003
Kähler parabolicity and the Euler number of compact manifolds of non-positive sectional curvature. Zbl 0992.53031
Cao, Jianguo; Xavier, Frederico
2001
Splittings and $$Cr$$-structures for manifolds with nonpositive sectional curvature. Zbl 1034.53038
Cao, Jianguo; Cheeger, Jeff; Rong, Xiaochun
2001
Cheeger isoperimetric constants of Gromov-hyperbolic spaces with quasi-poles. Zbl 0981.53021
Cao, Jianguo
2000
A new isoperimetric comparison theorem for surfaces of variable curvature. Zbl 0886.53031
Benjamini, Itai; Cao, Jianguo
1996
Examples of simply-connected Liouville manifolds with positive spectrum. Zbl 0861.53033
Benjamini, Itai; Cao, Jianguo
1996
Rigidity for non-compact surfaces of finite area and certain Kähler manifolds. Zbl 0845.57011
Cao, Jianguo
1995
The Ricci curvature equation with rotational symmetry. Zbl 0824.53034
Cao, Jianguo; DeTurck, Dennis
1994
The Bers-Nielsen kernels and souls of open surfaces with negatice curvature. Zbl 0799.30032
Cao, Jianguo
1994
Simple closed geodesics on convex surfaces. Zbl 0768.53019
Calabi, Eugenio; Cao, Jianguo
1992
The existence of generalized isothermal coordinates for higher dimensional Riemannian manifolds. Zbl 0715.53016
Cao, Jianguo
1991
Prescribing Ricci curvature on open surfaces. Zbl 0751.53014
Cao, Jianguo; DeTurck, Dennis
1991
all top 5

#### Cited by 186 Authors

 7 Pina, Romildo da Silva 6 Shaw, Mei-Chi 5 Saber, Sayed 4 Aubin, Thierry Émilien Flavien 4 Brinkschulte, Judith 4 Chang, Shu-Cheng 4 Huang, Teng 4 Tenenblat, Keti 4 Zhou, Xiangyu 3 Balacheff, Florent 3 Chiu, Hung-Lin 3 Fu, Siqi 3 Guan, Qi’an 3 Harrington, Phillip S. 3 Pieterzack, Mauricio 3 Tojeiro, Ruy 3 Wan, Xueyuan 3 Yang, Paul C. P. 3 Zhong, Chunping 2 Abdelkader, Osama 2 Adachi, Masanori 2 Bamler, Richard H. 2 Biard, Séverine 2 Binda, Federico 2 Cao, Huai-Dong 2 Cao, Jianguo 2 Chakrabarti, Debraj 2 Chanillo, Sagun 2 Chen, Bo-Yong 2 Chen, Chih-Wei 2 Deroin, Bertrand 2 Feng, Huitao 2 Ge, Jian 2 Hirachi, Kengo 2 Huang, Shaosai 2 Keller, Matthias 2 Li, Jinling 2 Li, YanYan 2 Liu, Kefeng 2 Martínez-Pérez, Álvaro 2 Marugame, Taiji 2 Morgan, Frank 2 Nardulli, Stefano 2 Ndiaye, Cheikh Birahim 2 Pansu, Pierre 2 Pulemotov, Artem 2 Ritoré, Manuel 2 Shioya, Takashi 2 Zhang, Lei 1 Abbondandolo, Alberto 1 Adriano, Levi 1 Akutagawa, Kazuo 1 Aldea, Nicoleta 1 Alexander, Stephanie B. 1 Álvarez Paiva, Juan Carlos 1 Beach, I. 1 Bei, Francesco 1 Belaïdi, Benharrat 1 Bessières, Laurent 1 Besson, Gérard 1 Bishop, Richard L. 1 Boileau, Michel Charles 1 Bramham, Barney 1 Brendle, Simon 1 Carron, Gilles 1 Case, Jeffrey S. 1 Chen, Qiyu 1 Colbois, Bruno 1 Connell, Chris 1 Disconzi, Marcelo Mendes 1 Dos Santos, João Paulo 1 Eichmair, Michael 1 Eschenburg, Jost-Hinrich 1 Esposito, Pierpaolo 1 Frauenfelder, Urs Adrian 1 Freitas, Pedro 1 Friedrich, Helmut 1 Grigor’yan, Alexander Asaturovich 1 Grimaldi, Renata 1 Grove, Karsten 1 Guler, Dincer 1 Han, Qi 1 Harman, Nate 1 Hattori, Tae 1 Hijazi, Oussama 1 Holopainen, Ilkka 1 Howards, Hugh Nelson 1 Howe, Sean 1 Hryniewicz, Umberto L. 1 Hutchings, Michael Lounsbery 1 Ida, Cristian 1 Iordan, Andrei 1 Itoh, Jin-ichi 1 Ivanov, Stefan P. 1 Ji, Ran 1 Jost, Jürgen 1 Kara, Mohamed Abdelhak 1 Kasue, Atsushi 1 Katmadas, Stefanos 1 Khidr, Shaban ...and 86 more Authors
all top 5

#### Cited in 65 Serials

 14 The Journal of Geometric Analysis 11 Mathematische Annalen 8 Advances in Mathematics 8 Transactions of the American Mathematical Society 6 Journal of Functional Analysis 6 Comptes Rendus. Mathématique. Académie des Sciences, Paris 5 Geometriae Dedicata 5 Journal für die Reine und Angewandte Mathematik 5 Mathematische Zeitschrift 5 Differential Geometry and its Applications 4 Proceedings of the American Mathematical Society 4 Annals of Global Analysis and Geometry 3 Communications in Mathematical Physics 3 Israel Journal of Mathematics 3 Journal of Geometry and Physics 3 Annales de l’Institut Fourier 3 Inventiones Mathematicae 3 Nagoya Mathematical Journal 3 Calculus of Variations and Partial Differential Equations 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Annali di Matematica Pura ed Applicata. Serie Quarta 2 Journal of Geometry 2 Osaka Journal of Mathematics 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Tohoku Mathematical Journal. Second Series 2 Revista Matemática Iberoamericana 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Bulletin of the American Mathematical Society. New Series 2 Acta Mathematica Sinica. English Series 2 International Journal of Geometric Methods in Modern Physics 2 Journal of Topology and Analysis 1 Indian Journal of Pure & Applied Mathematics 1 Journal of Mathematical Analysis and Applications 1 Periodica Mathematica Hungarica 1 Arkiv för Matematik 1 Acta Mathematica 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Canadian Mathematical Bulletin 1 Czechoslovak Mathematical Journal 1 Duke Mathematical Journal 1 Journal of Differential Equations 1 Journal of Pure and Applied Algebra 1 Manuscripta Mathematica 1 Mathematische Nachrichten 1 Michigan Mathematical Journal 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Publications of the Research Institute for Mathematical Sciences, Kyoto University 1 International Journal of Mathematics 1 Analele Ştiinţifice ale Universităţii Al. I. Cuza din Iaşi. Serie Nouă. Matematică 1 Journal of Algebraic Geometry 1 Bulletin des Sciences Mathématiques 1 Documenta Mathematica 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Geometry & Topology 1 Communications in Contemporary Mathematics 1 Journal of High Energy Physics 1 Milan Journal of Mathematics 1 Complex Variables and Elliptic Equations 1 Complex Analysis and Operator Theory 1 Asian-European Journal of Mathematics 1 Science China. Mathematics 1 Symmetry 1 European Journal of Mathematics 1 Transactions of A. Razmadze Mathematical Institute 1 Ural Mathematical Journal
all top 5

#### Cited in 26 Fields

 106 Differential geometry (53-XX) 61 Several complex variables and analytic spaces (32-XX) 31 Global analysis, analysis on manifolds (58-XX) 12 Calculus of variations and optimal control; optimization (49-XX) 12 Manifolds and cell complexes (57-XX) 10 Partial differential equations (35-XX) 7 Algebraic geometry (14-XX) 6 Dynamical systems and ergodic theory (37-XX) 5 Convex and discrete geometry (52-XX) 4 Functions of a complex variable (30-XX) 4 Potential theory (31-XX) 4 Relativity and gravitational theory (83-XX) 3 Combinatorics (05-XX) 3 Geometry (51-XX) 2 $$K$$-theory (19-XX) 2 Group theory and generalizations (20-XX) 2 Ordinary differential equations (34-XX) 2 Algebraic topology (55-XX) 1 Number theory (11-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Measure and integration (28-XX) 1 Functional analysis (46-XX) 1 Probability theory and stochastic processes (60-XX) 1 Fluid mechanics (76-XX) 1 Operations research, mathematical programming (90-XX)