从全纯函数到复流形(英文版)(From Holomorphic Functions to Complex Manifolds) 7510004713/978751000

《从全纯函数到复流形(英文版)》是一部介绍复流形理论的入门书籍。作者用尽可能简单的方法使读者熟悉多变量复分析中的重要分支和方法，所以避免出现比较抽象的概念，如，层、凝聚和高维上同调等，仅运用了基本方法幂级数、正则向量丛和一维上闭链。然而，解析集Remmert-Stein定理，正则向量丛中的截面空间有限定理以及Levi问题解这些深层次的都得到了完整的证明。每章的结束都有大量的例子和练习。具备实分析、代数、拓扑以及单变量理论知识就可以完全读懂这《从全纯函数到复流形(英文版)》。《从全纯函数到复流形(英文版)》可以作为学习多变量的入门教程，也是一本很好的参考书。 读者对象：《从全纯函数到复流形(英文版)》适用于数学专业的广大师生。 《从全纯函数到复流形(英文版)》是由世界图书出版公司出版的。 作者：(德国)弗里切(Fritzsche.K.) Preface Ⅰ Holomorphic Functions 1.Complex Geometry Real and Complex Structures Hermitian Forms and Inner Products Balls and Polydisks Connectedness Reinhardt Domains 2.Power Series Polynomials Convergence Power Series 3.Complex Differentiable Functions The Complex Gradient Weakly Holomorphic Functions Holomorphic Functions 4.The Cauchy Integral The Integral Formula Holomorphy of the Derivatives The Identity Theorem 5.The Hartogs Figure Expansion in Reinhardt Domains Hartogs Figures 6.The Cauchy-Riemann Equations Real Differentiable Functions Wirtinger's Calculus The Cauchy-Riemann Equations 7.Holomorphic Maps The Jacobian Chain Rules Tangent Vectors The Inverse Mapping 8.Analytic Sets Analytic Subsets Bounded Holomorphic Functions Regular Points Injective Holomorphic Mappings Ⅱ Domains of Holomorphy 1.The Continuity Theorem General Hartogs Figures Removable Singularities The Continuity Principle Hartogs Convexity Domains of Holomorphy 2.Plurisubharmonic Functions Subharmonic Functions The Maximum Principle Differentiable Subharmonic Functions Plurisubharmonic Functions The Levi Form Exhaustion Functions 3.Pseudoconvexity Pseudoconvexity The Boundary Distance Properties of Pseudoconvex Domains 4.Levi Convex Boundaries Boundary Functions The Levi Condition Affine Convexity A Theorem of Levi 5.Holomorphic Convexity Affine Convexity Holomorphic Convexity The Cartan-Thullen Theorem 6.Singular Functions Normal Exhaustions Unbounded Holomorphic Functions Sequences 7.Examples and Applications Domains of Holomorphy Complete Reinhardt Domains Analytic Polyhedra 8.Riemann Domains over Cn Riemann Domains Union of Riemann Domains 9.The Envelope of Holomorphy Holomorphy on Riemann Domains Envelopes of Holomorphy Pseudoconvexity Boundary Points Analytic Disks Ⅲ Analytic Sets 1.The Algebra of Power Series The Banach Algebra Bt Expansion with Respect to zt Convergent Series in Banach Algebras Convergent Power Series Distinguished Directions 2.The Preparation Theorem Division with Remainder in Bt The Weierstrass Condition Weierstrass Polynomials Weierstrass Preparation Theorem 3.Prime Factorization Unique Factorization Gauss's Lemma Factorization in Hn Hensel's Lemma The Noetherian Property 4.Branched Coverings Germs Pseudopolynomials Euclidean Domains The Algebraic Derivative Symmetric Polynomials The Discriminant Hypersurfaces The Unbranched Part Decompositions Projections 5.Irreducible Components Embedded-Analytic Sets Images of Embedded Analytic Sets Local Decomposition Analyticity The Zariski Topology Global Decompositions 6.Regular and Singular Points Compact Analytic Sets Embedding of Analytic Sets Regular Points of an Analytic Set The Singular Locus Extending Analytic Sets The Local Dimension Ⅳ Complex Manifolds 1.The Complex Structure Complex Coordinates Holomorphic Functions Riemann Surfaces Holomorphic Mappings Cartesian Products Analytic Subsets Differentiable Functions Tangent Vectors The Complex Structure on the Space of Derivations The Induced Mapping Immersions and Submersions Gluing 2.Complex Fiber Bundles Lie Groups and Transformation Grot ps Fiber Bt ndles Equivalence Complex Vector Bundles Standard Constructions Lifting of Bundles Subbundles and Quotients 3. Cehomolcgy Cohomology Groups Refinements Acyclic Coverings Generalizations The Singular Cohomology 4. Meromorphic Functions and Divisors The Ring of Germs Analytic Hypersurfaces Meromorphic Functions Divisors Associated Line Bundles Meromorphic Sections 5. Quotients and Submanifolds Topological Quotients Analytic Decompositions Properly Discontinuously Acting Groups Complex Tori Hopf Manifolds The Complex Projective Space Meromorphic Functions Grassmannian Manifolds Ⅴ Stein Theory Ⅵ Kahler Manifolds Ⅶ Boundary Behavior References Index of Notation Index The aim of this book is to give an understandable introduction to the the-ory of complex manifolds. With very few exceptions we give complete proofs.Many examples and figures along with quite a few exercises are included.Our intent is to familiarize the reader with the most important branches andmethods in complex analysis of several

ISBN	7510004713/978751000
出版社	世界图书出版公司
尺寸	24