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Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics (Record no. 10831)

MARC details
000 -LEADER
fixed length control field	04099nam a22005055i 4500
001 - CONTROL NUMBER
control field	978-3-642-23669-3
003 - CONTROL NUMBER IDENTIFIER
control field	DE-He213
005 - DATE AND TIME OF LATEST TRANSACTION
control field	20190213151501.0
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field	cr nn 008mamaa
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field	120104s2012 gw \| s \|\|\|\| 0\|eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number	9783642236693
--	978-3-642-23669-3
024 7# - OTHER STANDARD IDENTIFIER
Standard number or code	10.1007/978-3-642-23669-3
Source of number or code	doi
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number	QA331.7
072 #7 - SUBJECT CATEGORY CODE
Subject category code	PBKD
Source	bicssc
072 #7 - SUBJECT CATEGORY CODE
Subject category code	MAT034000
Source	bisacsh
072 #7 - SUBJECT CATEGORY CODE
Subject category code	PBKD
Source	thema
082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number	515.94
Edition number	23
245 10 - TITLE STATEMENT
Title	Complex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics
Medium	[electronic resource] /
Statement of responsibility, etc	edited by Vincent Guedj.
264 #1 -
--	Berlin, Heidelberg :
--	Springer Berlin Heidelberg,
--	2012.
300 ## - PHYSICAL DESCRIPTION
Extent	VIII, 310 p. 4 illus.
Other physical details	online resource.
336 ## -
--	text
--	txt
--	rdacontent
337 ## -
--	computer
--	c
--	rdamedia
338 ## -
--	online resource
--	cr
--	rdacarrier
347 ## -
--	text file
--	PDF
--	rda
490 1# - SERIES STATEMENT
Series statement	Lecture Notes in Mathematics,
International Standard Serial Number	0075-8434 ;
Volume number/sequential designation	2038
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note	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.
520 ## - SUMMARY, ETC.
Summary, etc	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 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Differential equations, partial.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Global differential geometry.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Geometry, algebraic.
650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Several Complex Variables and Analytic Spaces.
--	http://scigraph.springernature.com/things/product-market-codes/M12198
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Differential Geometry.
--	http://scigraph.springernature.com/things/product-market-codes/M21022
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Partial Differential Equations.
--	http://scigraph.springernature.com/things/product-market-codes/M12155
650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Algebraic Geometry.
--	http://scigraph.springernature.com/things/product-market-codes/M11019
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name	Guedj, Vincent.
Relator term	editor.
Relator code	edt
--	http://id.loc.gov/vocabulary/relators/edt
710 2# - ADDED ENTRY--CORPORATE NAME
Corporate name or jurisdiction name as entry element	SpringerLink (Online service)
773 0# - HOST ITEM ENTRY
Title	Springer eBooks
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text	Printed edition:
International Standard Book Number	9783642236686
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text	Printed edition:
International Standard Book Number	9783642236709
830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE
Uniform title	Lecture Notes in Mathematics,
--	0075-8434 ;
Volume number/sequential designation	2038
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier	https://doi.org/10.1007/978-3-642-23669-3
912 ## -
--	ZDB-2-SMA
912 ## -
--	ZDB-2-LNM

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