Description



Table of Contents
1. Differentiable Functions in Rn. Taylor's Formula. Partitions of Unity. Inverse Functions, Implicit Functions and the Rank Theorem. Sard's Theorem and Functional Dependence. Borel's Theorem on Taylor Series. Whitney's Approximation Theorem. An Approximation Theorem for Holomorphic Functions. Ordinary Differential Equations. 2. Manifolds. Basic Definitions. The Tangent and Cotangent Bundles. Grassmann Manifolds. Vector Fields and Differential Forms. Submanifolds. Exterior Differentiation. Orientation. Manifolds with Boundary. Integration. One Parameter Groups. The Frobenius Theorem. Almost Complex Manifolds. The Lemmata of Poincaré and Grothendieck. Applications: Hartog's Continuation Theorem and the Oka-Weil Theorem. Immersions and Imbeddings: Whitney's Theorems. Thom's Transversality Theorem. 3. Linear Elliptic Differential Operators. Vector Bundles. Fourier Transforms. Linear Differential Operators. The Sobolev Spaces. The Lemmata of Rellich and Sobolev. The Inequalities of Garding and Friedrichs. Elliptic Operators with C8 Coefficients: The Regularity Theorem. Elliptic Operators with Analytic Coefficients. The Finiteness Theorem. The Approximation Theorem and Its Application to Open Riemann Surfaces

Analysis on Real and Complex Manifolds

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    A Hardback by R. Narasimhan

    15 in stock


      View other formats and editions of Analysis on Real and Complex Manifolds by R. Narasimhan

      Publisher: Elsevier Science
      Publication Date: 12/1/1985 12:00:00 AM
      ISBN13: 9780444877765, 978-0444877765
      ISBN10: 0444877762
      Also in:
      Geometry

      Description



      Table of Contents
      1. Differentiable Functions in Rn. Taylor's Formula. Partitions of Unity. Inverse Functions, Implicit Functions and the Rank Theorem. Sard's Theorem and Functional Dependence. Borel's Theorem on Taylor Series. Whitney's Approximation Theorem. An Approximation Theorem for Holomorphic Functions. Ordinary Differential Equations. 2. Manifolds. Basic Definitions. The Tangent and Cotangent Bundles. Grassmann Manifolds. Vector Fields and Differential Forms. Submanifolds. Exterior Differentiation. Orientation. Manifolds with Boundary. Integration. One Parameter Groups. The Frobenius Theorem. Almost Complex Manifolds. The Lemmata of Poincaré and Grothendieck. Applications: Hartog's Continuation Theorem and the Oka-Weil Theorem. Immersions and Imbeddings: Whitney's Theorems. Thom's Transversality Theorem. 3. Linear Elliptic Differential Operators. Vector Bundles. Fourier Transforms. Linear Differential Operators. The Sobolev Spaces. The Lemmata of Rellich and Sobolev. The Inequalities of Garding and Friedrichs. Elliptic Operators with C8 Coefficients: The Regularity Theorem. Elliptic Operators with Analytic Coefficients. The Finiteness Theorem. The Approximation Theorem and Its Application to Open Riemann Surfaces

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