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Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics: 2038 (Lecture Notes in Mathematics, 2038) - Softcover
Synopsis
The purpose of these lecture notes is to provide an introduction to the theory of complex Monge-Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary).
These operators are of central use in several fundamental problems of complex differential geometry (Kähler-Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford-Taylor), Monge-Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi-Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli-Kohn-Nirenberg-Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong-Sturm and Berndtsson).
Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis.
"synopsis" may belong to another edition of this title.
- PublisherSpringer
- Publication date2012
- ISBN 10 3642236685
- ISBN 13 9783642236686
- BindingPaperback
- Number of pages318
- EditorGuedj Vincent
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Complex Monge¿Ampère Equations and Geodesics in the Space of Kähler Metrics
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Springer Berlin Heidelberg Jan 2012, 2012
ISBN 10: 3642236685
ISBN 13: 9783642236686
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -The purpose of these lecture notes is to provide an introduction to the theory of complex Monge-Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary).These operators are of central use in several fundamental problems of complex differential geometry (Kähler-Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford-Taylor), Monge-Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi-Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli-Kohn-Nirenberg-Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong-Sturm and Berndtsson).Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis. 320 pp. Englisch. Seller Inventory # 9783642236686
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Complex Monge: Ampere Equations and Geodesics in the Space of Kahler Metrics
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Complex Monge¿Ampère Equations and Geodesics in the Space of Kähler Metrics
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Springer Berlin Heidelberg, 2012
ISBN 10: 3642236685
ISBN 13: 9783642236686
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - The purpose of these lecture notes is to provide an introduction to the theory of complex Monge-Ampère operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Kähler manifolds (with or without boundary).These operators are of central use in several fundamental problems of complex differential geometry (Kähler-Einstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after Bedford-Taylor), Monge-Ampère foliations and laminated currents, polynomial hulls and Perron envelopes with no analytic structure, a self-contained presentation of Krylov regularity results, a modernized proof of the Calabi-Yau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Kähler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of Caffarelli-Kohn-Nirenberg-Spruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after Phong-Sturm and Berndtsson).Each chapter can be read independently and is based on a series of lectures by R. Berman, Z. Blocki, S. Boucksom, F. Delarue, R. Dujardin, B. Kolev and A. Zeriahi, delivered to non-experts. The book is thus addressed to any mathematician with some interest in one of the following fields, complex differential geometry, complex analysis, complex dynamics, fully non-linear PDE's and stochastic analysis. Seller Inventory # 9783642236686
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Complex Monge?Ampère Equations and Geodesics in the Space of Kähler Metrics (Lecture Notes in Mathematics, 2038)
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Complex Monge-Ampere Equations and Geodesics in the Space of Kahler Metrics
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