000 | 04099nam a22005055i 4500 | ||
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001 | 978-3-642-23669-3 | ||
003 | DE-He213 | ||
005 | 20190213151501.0 | ||
007 | cr nn 008mamaa | ||
008 | 120104s2012 gw | s |||| 0|eng d | ||
020 |
_a9783642236693 _9978-3-642-23669-3 |
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024 | 7 |
_a10.1007/978-3-642-23669-3 _2doi |
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050 | 4 | _aQA331.7 | |
072 | 7 |
_aPBKD _2bicssc |
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072 | 7 |
_aMAT034000 _2bisacsh |
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072 | 7 |
_aPBKD _2thema |
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082 | 0 | 4 |
_a515.94 _223 |
245 | 1 | 0 |
_aComplex Monge–Ampère Equations and Geodesics in the Space of Kähler Metrics _h[electronic resource] / _cedited by Vincent Guedj. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2012. |
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300 |
_aVIII, 310 p. 4 illus. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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338 |
_aonline resource _bcr _2rdacarrier |
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347 |
_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2038 |
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505 | 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-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 | _aThe 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 | _aDifferential equations, partial. | |
650 | 0 | _aGlobal differential geometry. | |
650 | 0 | _aGeometry, algebraic. | |
650 | 1 | 4 |
_aSeveral Complex Variables and Analytic Spaces. _0http://scigraph.springernature.com/things/product-market-codes/M12198 |
650 | 2 | 4 |
_aDifferential Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M21022 |
650 | 2 | 4 |
_aPartial Differential Equations. _0http://scigraph.springernature.com/things/product-market-codes/M12155 |
650 | 2 | 4 |
_aAlgebraic Geometry. _0http://scigraph.springernature.com/things/product-market-codes/M11019 |
700 | 1 |
_aGuedj, Vincent. _eeditor. _4edt _4http://id.loc.gov/vocabulary/relators/edt |
|
710 | 2 | _aSpringerLink (Online service) | |
773 | 0 | _tSpringer eBooks | |
776 | 0 | 8 |
_iPrinted edition: _z9783642236686 |
776 | 0 | 8 |
_iPrinted edition: _z9783642236709 |
830 | 0 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v2038 |
|
856 | 4 | 0 | _uhttps://doi.org/10.1007/978-3-642-23669-3 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
_c10831 _d10831 |