几何分析手册
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作者季理真 编
出版社高等教育出版社
ISBN9787040252880
出版时间2008-08
版次1
装帧精装
开本16开
纸张胶版纸
页数676页
字数99999千字
定价98元
上书时间2024-03-18
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基本信息
书名:几何分析手册
定价：98元
作者:季理真 编
出版社：高等教育出版社
出版日期：2008-08-01
ISBN：9787040252880
字数：820000
页码：676
版次：1
装帧：精装
开本：16开
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内容提要
Geometric Analysis combines differential equations and differential geometry。 Aimportant aspect is to solve geometric problems by studying differential equations。Besides some knowlinear differential operators such as the Laplace operator，many differential equations arising from differential geometry are nonlinear。 A particularly important example is the Monge-Ampere equation。 Applications to geometric problems have also motivated new methods and techniques idifferen-tial equations。 The field of geometric analysis is broad and has had many striking applications。 This handbook of geometric analysis provides introductions to and surveys of important topics igeometric analysis and their applications to related fields which is intend to be referred by graduate students and researchers irelated areas。
目录
Numerical Appromations to Extremal Metrics oToric SurfacesR.S.Bunch.SimoK.Donaldson1 Introduction2 The set-up2.1 Algebraic metrics2.2 Decompositioof the curvature tensor2.3 Integration3 Numerical algorithms：balanced metrics and refined appromations4 Numerical results4.1 The hexagon4.2 The pentagon4.3 The octagon4.4 The heptagon5 ConclusionsReferencesKaihler Geometry oToric Manifolds，and some other Manifolds with Large SymmetrySimoK.DonaldsonIntroduction1 Background1.1 Gauge theory and holomorphic bundles1.2 Symplectic and complex structures1.3 The equations2 Toric manifolds2.1 Local difierential geometry2.2 The global structure2.3 Algebraic metrics and asymptotics2.4 Extremal metrics otoric varieties3 Toric Fano manifolds3.1 The Kghler-Ricci solitoequation3.2 Continuity method，convety and a fundamental inequality3.3 A priori estimate3.4 The method of Wang and Zhu4 Variants of toric difierential geometry4.1 Multiplicity-free manifolds4.2 Manifolds with a dense orbit5 The Mukai-Umemura manifold and its deformations5.1 Mukai'S construction5.2 Topological and symplectic picture5.3 Defclrmations5.4 The a-invariantReferencesGluing Constructions of Special LagrangiaConesMark Haskins.Nikolaos Kapouleas1 Introduction2 Special Lagrangiacones and special Legendriasubmanifolds ofS2n-13 Cohomogeneity one special Legendriasubmanifolds of S2n-14 Constructioof the initial almost special Legendriasubmanifolds5 The symmetry group and the general framework for correcting the initial surfaces6 The linearized equation7 Using the Geometric Principle to prescribe the extended substitute kernel8 The mairesultsA Symmetries and quadraticsReferencesHarmonic MappingsJurgeJost1 Introduction2 Harmonic mappings from the perspective of Riemanniageometry2.1 Harmonic mappingetweeRiemanniamanifolds：definitions and properties2.2 The heat flow and harmonic mappings into nonpositively curved manifolds2.3 Harmonic mappings into convex regions and applications to the Bernsteiproblem3 Harmonic mappings from the perspective of abstract analysis and convety theory3.1 Estence3.2 Regularity3.3 Uniqueness and some applications4 Harmonic mappings iKghler and algebraic geometry4.1 Rigidity and superrigidity4.2 Harmonic maps and group representations4.3 Kghler groups4.4 Quasiprojective varieties and harmonic mappings of infinite energy5 Harmonic mappings and Riemansurfaces5.1 Families of Riemansurfaces……Harmonic Functions RiemanniaManifodldsComplety of Partial Differential EquationsVariational Principles oTriangulated SurfacesAsymptotic Structures ithe Geometry of Stability and Extremal MetricsStable Constant MeaCurvature SurfacesA General Asymptotic Decay Lemma for Elliptic ProblemsUniformizatioof OpeNonly Curved Kahler Manifolds iHigher DimensionsGeometry of Measures: Harmonic Analysis Meets Geometric Measure TheoryThe Monge-Ampere Eequatioand its Geometric AapplicationsLectures oMeaCurvature Flows iHigher CodimensionsLocal and Global Analysis of Eigenfunctions oRiemanniaManifoldsYau's Form of Schwarz Lemma and Arakelov Inequality OModuli Spaces of Projective Manifolds
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