## Warner, Frank W.

Compute Distance To:
 Author ID: warner.frank-w Published as: Warner, Frank W.; Warner, F. W.; Warner, Frank more...less External Links: MGP · Wikidata · GND · IdRef
 Documents Indexed: 24 Publications since 1965, including 3 Books 1 Further Contribution Co-Authors: 6 Co-Authors with 19 Joint Publications 198 Co-Co-Authors
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### Co-Authors

 5 single-authored 13 Kazdan, Jerry L. 5 Gluck, Herman 2 Ziller, Wolfgang 1 Alexander, Stephanie B. 1 Connelly, Robert 1 do Carmo, Manfredo Perdigão 1 Efimov, Nikolaĭ Vladimirovich 1 Jacobowitz, Howard 1 Khokhlov, Andreĭ Vladimirovich 1 Kolmogorov, Andreĭ Nikolaevich 1 Krigelman, Kenneth 1 Maltz, Robert 1 Moore, John Douglas 1 Novikov, Sergeĭ Petrovich 1 Sabitov, Idzhad Khakovich 1 Singer, David A. 1 Voronov, Theodore 1 Wallach, Nolan Russell 1 Yang, Chung-Tao
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### 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
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### Fields

 19 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

24 Publications have been cited 1,608 times in 1,434 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
A direct approach to the determination of Gaussian and scalar curvature functions. Zbl 0297.53021
Kazdan, Jerry L.; Warner, Frank W.
1975
Conjugate loci of constant order. Zbl 0172.23003
Warner, F. W.
1967
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
Integrability conditions for $$\Delta u = k - Ke^{\alpha u}$$ with applications to Riemannian geometry. Zbl 0218.35030
Kazdan, Jerry L.; Warner, Frank W.
1971
Curvature functions for 2-manifolds with negative Euler characteristic. Zbl 0255.53028
Kazdan, Jerry L.; Warner, Frank W.
1972
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. (Osnovy teorii gladkikh mnogoobrazij i grupp Li.) 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
Investigations in the metric theory of surfaces. Collection of articles. (Issledovaniya po metricheskoj teorii poverkhnostej. Sbornik statej). Transl. from the English and from the French by I.Kh.Sabitov. Zbl 0483.53001
1980
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. (Osnovy teorii gladkikh mnogoobrazij i grupp Li.) 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
Investigations in the metric theory of surfaces. Collection of articles. (Issledovaniya po metricheskoj teorii poverkhnostej. Sbornik statej). Transl. from the English and from the French by I.Kh.Sabitov. Zbl 0483.53001
1980
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
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### Cited by 1,648 Authors

 16 Pistoia, Angela 14 McKenna, Patrick Joseph 12 Ding, Shusen 12 Passaseo, Donato 11 Bartolucci, Daniele 11 Xing, Yuming 10 Musso, Monica 9 Molle, Riccardo 9 Yang, Yunyan 8 Gluck, Herman 8 Lazer, Alan C. 8 Mawhin, Jean L. 8 Xu, Xingwang 7 Chen, Wenxiong 7 Clapp, Mónica 7 de Marchis, Francesca 7 Del Pino, Manuel A. 7 Hirano, Norimichi 7 Jevnikar, Aleks 7 Yang, Yisong 7 Zhu, Xiaobao 6 Chang, Sun-Yung Alice 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 Ni, Wei-Ming 6 Rădulescu, Vicenţiu D. 6 Sánchez Caja, Miguel 6 Tunitskiĭ, Dmitriĭ Vasil’evich 6 Warner, Frank W. 5 Bandle, Catherine 5 Bianchi, Gabriele 5 Carlotto, Alessandro 5 Cavalcanti, Marcelo Moreira 5 Guedes de Figueiredo, Djairo 5 Domingos Cavalcanti, Valéria Neves 5 Fukuoka, Ryuichi 5 Grossi, Massimo 5 Gui, Changfeng 5 Kazdan, Jerry L. 5 Mancini, Giovanni 5 Peral Alonso, Ireneo 5 Piccione, Paolo 5 Rigoli, Marco 5 Rubio, Rafael María 5 Salvai, Marcos 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 Banyaga, Augustin 4 Ben Ayed, Mohamed 4 Chabrowski, Jan H. 4 Egnell, Henrik 4 Fischer, Arthur Elliot 4 Gamara, Najoua 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 Ngô Quốc Anh 4 Olver, Peter John 4 Palmer, Vicente 4 Pankka, Pekka 4 Parton, Maurizio 4 Piccinni, Paolo 4 Prástaro, Agostino 4 Rovenskiĭ, Vladimir Yuzefovich 4 Santra, Sanjiban 4 Schmidt, Benjamin 4 Shapiro, Victor L. 4 Shiohama, Katsuhiro 4 Solimini, Sergio 4 Struwe, Michael 4 Uǧuz, Selman 4 Ward, James Robert jun. 4 Yang, Wen 4 Yau, Shing-Tung 4 Zhu, Meijun 3 Amann, Herbert 3 Ammann, Bernd Eberhard 3 Anderson, Michael T. 3 Arcoya, David 3 Avalos, Rodrigo 3 Ayala, Victor ...and 1,548 more Authors
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### Cited in 314 Serials

 58 Journal of Differential Equations 53 Transactions of the American Mathematical Society 50 Calculus of Variations and Partial Differential Equations 47 Journal of Mathematical Analysis and Applications 47 Proceedings of the American Mathematical Society 44 Journal of Geometry and Physics 38 Communications in Mathematical Physics 36 The Journal of Geometric Analysis 36 Nonlinear Analysis. Theory, Methods & Applications 34 Mathematische Annalen 31 Annals of Global Analysis and Geometry 30 Journal of Functional Analysis 30 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 28 Duke Mathematical Journal 28 Differential Geometry and its Applications 26 Advances in Mathematics 23 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 Archive for Rational Mechanics and Analysis 15 Manuscripta Mathematica 14 Geometriae Dedicata 14 Linear Algebra and its Applications 13 Tohoku Mathematical Journal. Second Series 13 Journal of Mathematical Sciences (New York) 12 Journal de Mathématiques Pures et Appliquées. Neuvième Série 11 Communications in Contemporary Mathematics 10 Discrete and Continuous Dynamical Systems 9 General Relativity and Gravitation 9 Annales de l’Institut Fourier 9 Topology and its Applications 8 Computers & Mathematics with Applications 8 Annali di Matematica Pura ed Applicata. Serie Quarta 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 Reports on Mathematical Physics 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 Advanced Nonlinear Studies 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 Bulletin of the American Mathematical Society. New Series 5 Bulletin des Sciences Mathématiques 5 Annales Henri Poincaré 5 International Journal of Geometric Methods in Modern Physics 5 Science China. Mathematics 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 SIAM Journal on Control and Optimization 4 Probability Theory and Related Fields 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Annales de l’Institut Henri Poincaré. Physique Théorique 4 Potential Analysis 4 Geometry & Topology 4 Journal of Dynamical and Control Systems 3 Classical and Quantum Gravity 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 für die Reine und Angewandte Mathematik 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 Systems & Control Letters 3 Chinese Annals of Mathematics. Series B 3 International Journal of Mathematics 3 Geometric and Functional Analysis. GAFA 3 Annals of Physics 3 Sbornik: Mathematics 3 Journal of the European Mathematical Society (JEMS) 3 Journal of the Australian Mathematical Society 3 Communications on Pure and Applied Analysis 3 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 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 ...and 214 more Serials
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### Cited in 59 Fields

 620 Differential geometry (53-XX) 497 Partial differential equations (35-XX) 393 Global analysis, analysis on manifolds (58-XX) 107 Manifolds and cell complexes (57-XX) 75 Quantum theory (81-XX) 71 Dynamical systems and ergodic theory (37-XX) 67 Topological groups, Lie groups (22-XX) 67 Operator theory (47-XX) 58 Ordinary differential equations (34-XX) 56 Several complex variables and analytic spaces (32-XX) 54 Functional analysis (46-XX) 54 Relativity and gravitational theory (83-XX) 50 Algebraic topology (55-XX) 45 Algebraic geometry (14-XX) 37 Calculus of variations and optimal control; optimization (49-XX) 37 Systems theory; control (93-XX) 33 Probability theory and stochastic processes (60-XX) 33 Mechanics of particles and systems (70-XX) 27 Functions of a complex variable (30-XX) 25 Linear and multilinear algebra; matrix theory (15-XX) 24 Numerical analysis (65-XX) 22 Fluid mechanics (76-XX) 20 Nonassociative rings and algebras (17-XX) 20 Potential theory (31-XX) 18 Real functions (26-XX) 17 Abstract harmonic analysis (43-XX) 16 Mechanics of deformable solids (74-XX) 15 Group theory and generalizations (20-XX) 15 Geometry (51-XX) 15 Convex and discrete geometry (52-XX) 12 Biology and other natural sciences (92-XX) 10 Measure and integration (28-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Category theory; homological algebra (18-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 9 General topology (54-XX) 9 Statistics (62-XX) 8 Optics, electromagnetic theory (78-XX) 7 Number theory (11-XX) 6 Combinatorics (05-XX) 6 Special functions (33-XX) 6 Integral transforms, operational calculus (44-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Associative rings and algebras (16-XX) 5 Computer science (68-XX) 4 History and biography (01-XX) 4 Mathematical logic and foundations (03-XX) 4 Integral equations (45-XX) 3 Field theory and polynomials (12-XX) 3 Operations research, mathematical programming (90-XX) 2 Commutative algebra (13-XX) 2 Difference and functional equations (39-XX) 2 Approximations and expansions (41-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Geophysics (86-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Astronomy and astrophysics (85-XX)

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