Analysis on real and complex manifolds /
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| Author / Creator: | Narasimhan, Raghavan |
|---|---|
| Imprint: | Amsterdam ; New York : North-Holland ; New York, N.Y. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1985, c1968. |
| Description: | xiv, 246 p. ; 23 cm. |
| Language: | English |
| Series: | North-Holland mathematical library v. 35 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/745286 |
Table of Contents:
- Chapters
- 1. Differentiable Functions in R n
- 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 Poincare 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 C infin; Coefficients: The Regularity Theorem
- Elliptic Operators with Analytic Coefficients
- The Finiteness Theorem
- The Approximation Theorem and Its Application to Open Riemann Surfaces
- References
- Subject Index