000			03846nam a22005175i 4500
003			DE-He213
005			20191014014832.0
007			cr nn 008mamaa
008			120104s2012 gw | s |||| 0|eng d
020	6	4	_a9783642236693 _9978-3-642-23669-3
024	8	7	_a10.1007/978-3-642-23669-3 _2doi
050	8	4	_aQA331.7
072	8	7	_aPBKD _2bicssc
072	8	7	_aMAT034000 _2bisacsh
082			_a515.94 _223
100	8	1	_aGuedj, Vincent. _eeditor. _9183581
245	9	7	_aComplex MongeAmpȿre Equations and Geodesics in the Space of Khler Metrics _h[electronic resource] / _cedited by Vincent Guedj.
001			000070819
300	6	4	_aVIII, 310p. 4 illus. _bonline resource.
490	8	1	_aLecture Notes in Mathematics, _x0075-8434 ; _v2038
505	8	0	_a1.Introduction -- I. The Local Homogenious Dirichlet Problem.-2. Dirichlet Problem in Domains of Cn -- 3. Geometric Maximality -- II. Stochastic Analysis for the Monge-Ampȿre Equation -- 4. Probabilistic Approach to Regularity -- III. Monge-Ampȿre Equations on Compact Manifolds -- 5.The Calabi-Yau Theorem -- IV Geodesics in the Space of Khler Metrics -- 6. The Riemannian Space of Khler Metrics -- 7. MA Equations on Manifolds with Boundary -- 8. Bergman Geodesics.
520	6	4	_aThe purpose of these lecture notes is to provide an introduction to the theory of complex MongeAmpȿre operators (definition, regularity issues, geometric properties of solutions, approximation) on compact Khler manifolds (with or without boundary). These operators are of central use in several fundamental problems of complex differential geometry (KhlerEinstein equation, uniqueness of constant scalar curvature metrics), complex analysis and dynamics. The topics covered include, the Dirichlet problem (after BedfordTaylor), MongeAmpȿre 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 CalabiYau theorem (after Yau and Kolodziej), an introduction to infinite dimensional riemannian geometry, geometric structures on spaces of Khler metrics (after Mabuchi, Semmes and Donaldson), generalizations of the regularity theory of CaffarelliKohnNirenbergSpruck (after Guan, Chen and Blocki) and Bergman approximation of geodesics (after PhongSturm and Berndtsson). Each chapter can be read independently and is based on a series of lectures byR. 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	8	0	_aMathematics. _98571
650	8	0	_aGeometry, algebraic. _9183582
650	8	0	_aDifferential equations, partial. _99614
650	8	0	_aGlobal differential geometry. _99530
650			_aMathematics. _98571
650			_aSeveral Complex Variables and Analytic Spaces. _912257
650			_aDifferential Geometry. _99532
650			_aPartial Differential Equations. _99616
650			_aAlgebraic Geometry. _9183583
710	8	2	_aSpringerLink (Online service) _9183584
773	8	0	_tSpringer eBooks
776			_iPrinted edition: _z9783642236686
830	8	0	_aLecture Notes in Mathematics, _x0075-8434 ; _v2038 _9183585
856			_uhttp://dx.doi.org/10.1007/978-3-642-23669-3 _zde clik aquí para ver el libro electrónico
264	8	1	_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2012.
336	6	4	_atext _btxt _2rdacontent
337	6	4	_acomputer _bc _2rdamedia
338	6	4	_aonline resource _bcr _2rdacarrier
347	6	4	_atext file _bPDF _2rda
516	6	4	_aZDB-2-SMA
516	6	4	_aZDB-2-LNM
999			_c70549 _d70549
942			_c05