# zbMATH — the first resource for mathematics

## Warner, Frank W.

Compute Distance To:
 Author ID: warner.frank-w Published as: Warner, F. W.; Warner, Frank; Warner, Frank W. External Links: MGP · Wikidata · GND
 Documents Indexed: 24 Publications since 1965, including 3 Books
all top 5

#### Co-Authors

 6 single-authored 12 Kazdan, Jerry L. 4 Gluck, Herman 2 Ziller, Wolfgang 1 do Carmo, Manfredo Perdigão 1 Wallach, Nolan Russell 1 Yang, Chung-Tao
all top 5

#### Serials

 4 Annals of Mathematics. Second Series 3 Proceedings of the American Mathematical Society 2 Duke Mathematical Journal 2 Journal of Differential Geometry 2 Bulletin of the American Mathematical Society 1 Communications on Pure and Applied Mathematics 1 American Journal of Mathematics 1 Inventiones Mathematicae 1 Transactions of the American Mathematical Society 1 Annals of Global Analysis and Geometry 1 L’Enseignement Mathématique. 2e Série 1 Graduate Texts in Mathematics
all top 5

#### Fields

 18 Differential geometry (53-XX) 10 Partial differential equations (35-XX) 9 Global analysis, analysis on manifolds (58-XX) 4 Algebraic topology (55-XX) 3 Topological groups, Lie groups (22-XX) 2 Manifolds and cell complexes (57-XX)

#### Citations contained in zbMATH Open

23 Publications have been cited 1,541 times in 1,380 Documents Cited by Year
Foundations of differentiable manifolds and Lie groups. Reprint. Zbl 0516.58001
Warner, Frank W.
1983
Curvature functions for compact 2-manifolds. Zbl 0273.53034
Kazdan, Jerry L.; Warner, Frank W.
1974
Foundations of differentiable manifolds and Lie groups. Zbl 0241.58001
Warner, Frank W.
1971
Remarks on some quasilinear elliptic equations. Zbl 0325.35038
Kazdan, Jerry L.; Warner, Frank W.
1975
Scalar curvature and conformal deformation of Riemannian structure. Zbl 0296.53037
Kazdan, Jerry L.; Warner, Frank W.
1975
Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures. Zbl 0297.53020
Kazdan, Jerry L.; Warner, Frank W.
1975
Curvature functions for open 2-manifolds. Zbl 0278.53031
Kazdan, Jerry L.; Warner, Frank W.
1974
Rigidity and convexity of hypersurfaces in spheres. Zbl 0201.23702
do Carmo, Manfredo Perdigão; Warner, F. W.
1970
The conjugate locus of a Riemannian manifold. Zbl 0129.36002
Warner, F. W.
1965
Extension of the Rauch comparison theorem to submanifolds. Zbl 0139.15601
Warner, F. W.
1966
Great circle fibrations of the three-sphere. Zbl 0523.55020
Gluck, Herman; Warner, Frank W.
1983
The geometry of the Hopf fibrations. Zbl 0616.53038
Gluck, Herman; Warner, Frank; Ziller, Wolfgang
1986
Prescribing curvatures. Zbl 0313.53017
Kazdan, Jerry L.; Warner, Frank W.
1975
Conjugate loci of constant order. Zbl 0172.23003
Warner, F. W.
1967
A direct approach to the determination of Gaussian and scalar curvature functions. Zbl 0297.53021
Kazdan, Jerry L.; Warner, Frank W.
1975
Division algebras, fibrations of spheres by great spheres and the topological determination of space by the gross behavior of its geodesics. Zbl 0534.53039
Gluck, Herman; Warner, Frank; Yang, C. T.
1983
Fibrations of spheres by parallel great spheres and Berger’s rigidity theorem. Zbl 0642.53046
Gluck, Herman; Warner, Frank; Ziller, Wolfgang
1987
Curvature forms for 2-manifolds. Zbl 0197.47901
Wallach, N. R.; Warner, F. W.
1970
Curvature functions for 2-manifolds with negative Euler characteristic. Zbl 0255.53028
Kazdan, Jerry L.; Warner, Frank W.
1972
Integrability conditions for $$\Delta u = k - Ke^{\alpha u}$$ with applications to Riemannian geometry. Zbl 0218.35030
Kazdan, Jerry L.; Warner, Frank W.
1971
Foundations of differentiable manifolds and Lie groups. (Osnovy teorii gladkikh mnogoobrazij i grupp Li). Transl. from the English by F. F. Voronov and A. V. Khokhlov. Transl. ed. and with a preface by A. A. Kirillov. Zbl 0691.58005
Warner, Frank W.
1987
Surfaces of revolution with monotonic increasing curvature and an application to the equation $$\Delta u = 1 - Ke^{2 u}$$ on $$S^ 2$$. Zbl 0228.53004
Kazdan, Jerry L.; Warner, Frank W.
1972
Curvature functions for 2-manifolds. Zbl 0261.53047
Kazdan, Jerry L.; Warner, Frank W.
1973
Fibrations of spheres by parallel great spheres and Berger’s rigidity theorem. Zbl 0642.53046
Gluck, Herman; Warner, Frank; Ziller, Wolfgang
1987
Foundations of differentiable manifolds and Lie groups. (Osnovy teorii gladkikh mnogoobrazij i grupp Li). Transl. from the English by F. F. Voronov and A. V. Khokhlov. Transl. ed. and with a preface by A. A. Kirillov. Zbl 0691.58005
Warner, Frank W.
1987
The geometry of the Hopf fibrations. Zbl 0616.53038
Gluck, Herman; Warner, Frank; Ziller, Wolfgang
1986
Foundations of differentiable manifolds and Lie groups. Reprint. Zbl 0516.58001
Warner, Frank W.
1983
Great circle fibrations of the three-sphere. Zbl 0523.55020
Gluck, Herman; Warner, Frank W.
1983
Division algebras, fibrations of spheres by great spheres and the topological determination of space by the gross behavior of its geodesics. Zbl 0534.53039
Gluck, Herman; Warner, Frank; Yang, C. T.
1983
Remarks on some quasilinear elliptic equations. Zbl 0325.35038
Kazdan, Jerry L.; Warner, Frank W.
1975
Scalar curvature and conformal deformation of Riemannian structure. Zbl 0296.53037
Kazdan, Jerry L.; Warner, Frank W.
1975
Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures. Zbl 0297.53020
Kazdan, Jerry L.; Warner, Frank W.
1975
Prescribing curvatures. Zbl 0313.53017
Kazdan, Jerry L.; Warner, Frank W.
1975
A direct approach to the determination of Gaussian and scalar curvature functions. Zbl 0297.53021
Kazdan, Jerry L.; Warner, Frank W.
1975
Curvature functions for compact 2-manifolds. Zbl 0273.53034
Kazdan, Jerry L.; Warner, Frank W.
1974
Curvature functions for open 2-manifolds. Zbl 0278.53031
Kazdan, Jerry L.; Warner, Frank W.
1974
Curvature functions for 2-manifolds. Zbl 0261.53047
Kazdan, Jerry L.; Warner, Frank W.
1973
Curvature functions for 2-manifolds with negative Euler characteristic. Zbl 0255.53028
Kazdan, Jerry L.; Warner, Frank W.
1972
Surfaces of revolution with monotonic increasing curvature and an application to the equation $$\Delta u = 1 - Ke^{2 u}$$ on $$S^ 2$$. Zbl 0228.53004
Kazdan, Jerry L.; Warner, Frank W.
1972
Foundations of differentiable manifolds and Lie groups. Zbl 0241.58001
Warner, Frank W.
1971
Integrability conditions for $$\Delta u = k - Ke^{\alpha u}$$ with applications to Riemannian geometry. Zbl 0218.35030
Kazdan, Jerry L.; Warner, Frank W.
1971
Rigidity and convexity of hypersurfaces in spheres. Zbl 0201.23702
do Carmo, Manfredo Perdigão; Warner, F. W.
1970
Curvature forms for 2-manifolds. Zbl 0197.47901
Wallach, N. R.; Warner, F. W.
1970
Conjugate loci of constant order. Zbl 0172.23003
Warner, F. W.
1967
Extension of the Rauch comparison theorem to submanifolds. Zbl 0139.15601
Warner, F. W.
1966
The conjugate locus of a Riemannian manifold. Zbl 0129.36002
Warner, F. W.
1965
all top 5

#### Cited by 1,632 Authors

 15 Pistoia, Angela 14 McKenna, Patrick Joseph 11 Bartolucci, Daniele 11 Ding, Shusen 10 Passaseo, Donato 10 Xing, Yuming 9 Musso, Monica 8 Gluck, Herman 8 Lazer, Alan C. 8 Mawhin, Jean L. 7 Chen, Wenxiong 7 Clapp, Mónica 7 de Marchis, Francesca 7 Del Pino, Manuel A. 7 Hirano, Norimichi 7 Jevnikar, Aleks 7 Molle, Riccardo 7 Xu, Xingwang 7 Yang, Yisong 6 Chtioui, Hichem 6 Espinar, José María 6 Ge, Huabin 6 Abreu Goncalves, Jose Valdo 6 Grasse, Kevin A. 6 Hebey, Emmanuel 6 Ho, Pak Tung 6 Javaloyes, Miguel Angel 6 Li, Congming 6 Li, YanYan 6 Malchiodi, Andrea 6 Mancini, Giovanni 6 Ni, Wei-Ming 6 Sánchez Caja, Miguel 6 Tunitskij, Dmitry Vasilievich 6 Warner, Frank W. 6 Yang, Yunyan 6 Zhu, Xiaobao 5 Bandle, Catherine 5 Cavalcanti, Marcelo Moreira 5 Chang, Sun-Yung Alice 5 Guedes de Figueiredo, Djairo 5 Domingos Cavalcanti, Valéria Neves 5 Grossi, Massimo 5 Kazdan, Jerry L. 5 Peral Alonso, Ireneo 5 Piccione, Paolo 5 Prykarpatsky, Anatoliy Karolevych 5 Prykarpatsky, Yarema Anatoliyovych 5 Rădulescu, Vicenţiu D. 5 Rigoli, Marco 5 Schoen, Richard Melvin 5 Suzuki, Takashi 5 Wang, Guofang 5 Wei, Juncheng 5 Wolansky, Gershon 5 Yang, Paul C. P. 4 Ambrosetti, Antonio 4 Ayala, Victor 4 Banyaga, Augustin 4 Ben Ayed, Mohamed 4 Bianchi, Gabriele 4 Carlotto, Alessandro 4 Chabrowski, Jan H. 4 Egnell, Henrik 4 Fischer, Arthur Elliot 4 Fukuoka, Ryuichi 4 Gamara, Najoua 4 Gui, Changfeng 4 Han, Zheng-Chao 4 Helminck, Gerardus Franciscus 4 Jung, Yoon-Tae 4 Kiessling, Michael Karl-Heinz 4 Li, Jiayu 4 Markvorsen, Steen 4 Monterde, Juan 4 Moretti, Valter 4 Ngo, Quoc Anh 4 Olver, Peter John 4 Palmer, Vicente 4 Pankka, Pekka 4 Prástaro, Agostino 4 Rovenskiĭ, Vladimir Yuzefovich 4 Salvai, Marcos 4 Samoĭlenko, Anatoliĭ Mykhaĭlovych 4 Santra, Sanjiban 4 Schmidt, Benjamin 4 Shapiro, Victor L. 4 Shiohama, Katsuhiro 4 Solimini, Sergio 4 Struwe, Michael 4 Uǧuz, Selman 4 Vaugon, Michel 4 Ward, James Robert jun. 4 Yang, Wen 4 Yau, Shing-Tung 4 Zhu, Meijun 3 Amann, Herbert 3 Ammann, Bernd Eberhard 3 Arcoya, David 3 Avalos, Rodrigo ...and 1,532 more Authors
all top 5

#### Cited in 298 Serials

 57 Journal of Differential Equations 53 Transactions of the American Mathematical Society 46 Journal of Mathematical Analysis and Applications 46 Journal of Geometry and Physics 46 Proceedings of the American Mathematical Society 45 Calculus of Variations and Partial Differential Equations 38 Communications in Mathematical Physics 38 Nonlinear Analysis. Theory, Methods & Applications 34 Mathematische Annalen 31 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 30 The Journal of Geometric Analysis 29 Journal of Functional Analysis 28 Annals of Global Analysis and Geometry 28 Differential Geometry and its Applications 27 Duke Mathematical Journal 23 Advances in Mathematics 22 Mathematische Zeitschrift 21 Journal of Mathematical Physics 21 Communications in Partial Differential Equations 18 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 16 Inventiones Mathematicae 15 Manuscripta Mathematica 14 Archive for Rational Mechanics and Analysis 14 Linear Algebra and its Applications 13 Journal of Mathematical Sciences (New York) 12 Geometriae Dedicata 12 Tohoku Mathematical Journal. Second Series 12 Journal de Mathématiques Pures et Appliquées. Neuvième Série 11 Annali di Matematica Pura ed Applicata. Serie Quarta 10 Discrete and Continuous Dynamical Systems 10 Communications in Contemporary Mathematics 9 Computers & Mathematics with Applications 9 Annales de l’Institut Fourier 8 General Relativity and Gravitation 8 Reports on Mathematical Physics 8 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 8 Mathematische Nachrichten 8 Results in Mathematics 8 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 7 International Journal of Theoretical Physics 7 Topology and its Applications 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 7 Bulletin of the American Mathematical Society 6 Mathematical Notes 6 Nuclear Physics. B 6 Algebraic & Geometric Topology 6 Bulletin of the Brazilian Mathematical Society. New Series 5 Archiv der Mathematik 5 Compositio Mathematica 5 Rendiconti del Seminario Matematico della Università di Padova 5 Systems & Control Letters 5 Bulletin of the American Mathematical Society. New Series 5 Journal of High Energy Physics 5 Annales Henri Poincaré 5 International Journal of Geometric Methods in Modern Physics 4 Applicable Analysis 4 Israel Journal of Mathematics 4 Reviews in Mathematical Physics 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie IV 4 Journal of Soviet Mathematics 4 Monatshefte für Mathematik 4 Probability Theory and Related Fields 4 Annals of Physics 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Annales de l’Institut Henri Poincaré. Physique Théorique 4 Bulletin des Sciences Mathématiques 4 Geometry & Topology 4 Journal of Dynamical and Control Systems 4 Advanced Nonlinear Studies 3 Communications on Pure and Applied Mathematics 3 Journal d’Analyse Mathématique 3 Linear and Multilinear Algebra 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Rocky Mountain Journal of Mathematics 3 The Mathematical Intelligencer 3 Boletim da Sociedade Brasileira de Matemática 3 Journal of Computational and Applied Mathematics 3 Journal of Multivariate Analysis 3 Memoirs of the American Mathematical Society 3 Nagoya Mathematical Journal 3 Proceedings of the Edinburgh Mathematical Society. Series II 3 Proceedings of the Japan Academy. Series A 3 Rendiconti del Circolo Matemàtico di Palermo. Serie II 3 Chinese Annals of Mathematics. Series B 3 International Journal of Mathematics 3 Geometric and Functional Analysis. GAFA 3 Potential Analysis 3 Sbornik: Mathematics 3 Journal of the European Mathematical Society (JEMS) 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 Science China. Mathematics 2 Bulletin of the Australian Mathematical Society 2 Computer Methods in Applied Mechanics and Engineering 2 Discrete Mathematics 2 International Journal of Control 2 Journal of Statistical Physics 2 Mathematical Methods in the Applied Sciences 2 Theoretical and Mathematical Physics 2 Ukrainian Mathematical Journal 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik ...and 198 more Serials
all top 5

#### Cited in 59 Fields

 582 Differential geometry (53-XX) 467 Partial differential equations (35-XX) 374 Global analysis, analysis on manifolds (58-XX) 104 Manifolds and cell complexes (57-XX) 75 Quantum theory (81-XX) 70 Dynamical systems and ergodic theory (37-XX) 65 Operator theory (47-XX) 62 Ordinary differential equations (34-XX) 61 Topological groups, Lie groups (22-XX) 55 Several complex variables and analytic spaces (32-XX) 54 Relativity and gravitational theory (83-XX) 52 Functional analysis (46-XX) 48 Algebraic topology (55-XX) 40 Algebraic geometry (14-XX) 39 Systems theory; control (93-XX) 34 Calculus of variations and optimal control; optimization (49-XX) 34 Probability theory and stochastic processes (60-XX) 33 Mechanics of particles and systems (70-XX) 29 Numerical analysis (65-XX) 25 Linear and multilinear algebra; matrix theory (15-XX) 24 Functions of a complex variable (30-XX) 21 Fluid mechanics (76-XX) 19 Nonassociative rings and algebras (17-XX) 19 Potential theory (31-XX) 17 Abstract harmonic analysis (43-XX) 17 Mechanics of deformable solids (74-XX) 14 Real functions (26-XX) 13 Group theory and generalizations (20-XX) 12 Geometry (51-XX) 12 Convex and discrete geometry (52-XX) 11 Biology and other natural sciences (92-XX) 10 Measure and integration (28-XX) 10 Harmonic analysis on Euclidean spaces (42-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Category theory; homological algebra (18-XX) 9 General topology (54-XX) 9 Statistics (62-XX) 8 Number theory (11-XX) 8 Optics, electromagnetic theory (78-XX) 7 Special functions (33-XX) 6 Combinatorics (05-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Associative rings and algebras (16-XX) 5 Integral transforms, operational calculus (44-XX) 5 Integral equations (45-XX) 4 History and biography (01-XX) 4 Mathematical logic and foundations (03-XX) 4 Computer science (68-XX) 3 Approximations and expansions (41-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 2 Difference and functional equations (39-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Operations research, mathematical programming (90-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Astronomy and astrophysics (85-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX)

#### Wikidata Timeline

The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.