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...
Guardat en:
| Altres autors: | |
|---|---|
| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2012. |
| Col·lecció: | Lecture Notes in Mathematics
2038 |
| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
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 |
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| 245 | 0 | 0 | |a Complex Monge Ampère Equations and Geodesics in the Space of Kähler Metrics |c Vincent Guedj., editor. |
| 250 | |a 1st ed. 2012. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 1 | |a Lecture Notes in Mathematics |v 2038 |x 1617-9692 | |
| 500 | |a L'impression du document génère 310 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. | ||
| 505 | 1 | |a 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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. | ||
| 650 | |a Équations de Monge-Ampère | ||
| 650 | |a Géodésiques (mathématiques) | ||
| 650 | |a Structures kählériennes | ||
| 650 | |a Géométrie différentielle globale | ||
| 650 | |a Équations aux dérivées partielles | ||
| 650 | |a Géométrie différentielle | ||
| 650 | |a Mathématiques | ||
| 650 | |a Géométrie algébrique | ||
| 650 | |a Fonctions de plusieurs variables complexes | ||
| 650 | |a Actes de congrès | ||
| 700 | 1 | |a Guedj, Vincent, |d 19..-...., |c mathématicien. |4 pbd | |
| 776 | 0 | |0 158096134 |t Complex Monge-Ampère equations and geodesics in the space of Kähler metrics |f Vincent Guedj, editor |c Heidelberg |n Springer |d 2012 |p 1 vol. (VIII-310 p.) |s Lecture notes in mathematics |z 978-3-642-23668-6 | |
| 776 | 0 | |0 158096134 |t Complex Monge-Ampère equations and geodesics in the space of Kähler metrics |f Vincent Guedj, editor |c Heidelberg |n Springer |d 2012 |p 1 vol. (VIII-310 p.) |s Lecture notes in mathematics |z 978-3-642-23668-6 | |
| 776 | 0 | |t Complex Monge-Ampère Equations and Geodesics in the Space of Kähler Metrics |b Texte imprimé |z 9783642236709 | |
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| 997 | |0 974128 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||