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Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics [[electronic resource] /] / edited by Vincent Guedj



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Titolo: Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics [[electronic resource] /] / edited by Vincent Guedj Visualizza cluster
Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2012
Edizione: 1st ed. 2012.
Descrizione fisica: 1 online resource (VIII, 310 p. 4 illus.)
Disciplina: 515/.7242
Soggetto topico: Functions of complex variables
Differential geometry
Partial differential equations
Algebraic geometry
Several Complex Variables and Analytic Spaces
Differential Geometry
Partial Differential Equations
Algebraic Geometry
Soggetto genere / forma: Aufsatzsammlung
Classificazione: SI 850
MAT 146f
MAT 322f
MAT 354f
MAT 537f
510
Persona (resp. second.): GuedjVincent
Note generali: Bibliographic Level Mode of Issuance: Monograph
Nota di bibliografia: Includes bibliographical references.
Nota di contenuto: 1.Introduction -- I. The Local Homogenious Dirichlet Problem.-2. Dirichlet Problem in Domains of Cn -- 3. Geometric Maximality -- II. Stochastic Analysis for the Monge-Ampère Equation -- 4. Probabilistic Approach to Regularity -- III. Monge-Ampère Equations on Compact Manifolds -- 5.The Calabi-Yau Theorem -- IV Geodesics in the Space of Kähler Metrics -- 6. The Riemannian Space of Kähler Metrics -- 7. MA Equations on Manifolds with Boundary -- 8. Bergman Geodesics.
Sommario/riassunto: 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.
Titolo autorizzato: Complex Monge–Ampère equations and geodesics in the space of Kähler metrics  Visualizza cluster
ISBN: 3-642-23669-3
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 996466663503316
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Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 2038