Complex Monge Ampère Equations and Geodesics in the Space of Kähler Metrics
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 fun...
में बचाया:
| अन्य लेखक: | |
|---|---|
| स्वरूप: | Livre numérique |
| भाषा: | Anglais |
| प्रकाशित: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| संस्करण: | 1st ed. 2012. |
| श्रृंखला: | Lecture Notes in Mathematics
2038 |
| विषय: | |
| ऑनलाइन पहुंच: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| टिप्पणी: |
L'impression du document génère 310 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Complex Monge-Ampère equations and geodesics in the space of Kähler metrics, Vincent Guedj, editor, Heidelberg, Springer, 2012, 1 vol. (VIII-310 p.), Lecture notes in mathematics, 978-3-642-23668-6 • Complex Monge-Ampère equations and geodesics in the space of Kähler metrics, Vincent Guedj, editor, Heidelberg, Springer, 2012, 1 vol. (VIII-310 p.), Lecture notes in mathematics, 978-3-642-23668-6 • Complex Monge-Ampère Equations and Geodesics in the Space of Kähler Metrics, Texte imprimé, 9783642236709 |
| सारांश: | 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. |
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| वस्तु वर्णन: | L'impression du document génère 310 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ग्रन्थसूची: | Bibliogr. |
| आईएसबीएन: | 9783642236693 |
| आईएसएसएन: | 1617-9692 |
| अभिगमन: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |