| 书目名称 | Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics | | 编辑 | Vincent Guedj | | 视频video | http://file.papertrans.cn/232/231473/231473.mp4 | | 概述 | The first self contained presentation of Krylov‘s stochastic analysis for the complex Monge-Ampere equation.A comprehensive presentation of Yau‘s proof of the Calabi conjecture.A great part of the mat | | 丛书名称 | Lecture Notes in Mathematics | | 图书封面 |  | | 描述 | .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, | | 出版日期 | Book 2012 | | 关键词 | 32-XX, 53-XX, 35-XX, 14-XX; Complex Monge-Ampere equations; Geodesics in the space of Kaehler metrics; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-23669-3 | | isbn_softcover | 978-3-642-23668-6 | | isbn_ebook | 978-3-642-23669-3Series ISSN 0075-8434 Series E-ISSN 1617-9692 | | issn_series | 0075-8434 | | copyright | Springer-Verlag Berlin Heidelberg 2012 |
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