Analysis on Real and Complex Manifolds: Volume 35
2nd Edition
Published on 1. December 1985
Book
Hardback
245 pages
978-0-444-87776-5 (ISBN)
Description
Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sard's theorem and Whitney's approximation theorem.
The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincare and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem.
Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein.
The next chapter is an introduction to real and complex manifolds. It contains an exposition of the theorem of Frobenius, the lemmata of Poincare and Grothendieck with applications of Grothendieck's lemma to complex analysis, the imbedding theorem of Whitney and Thom's transversality theorem.
Chapter 3 includes characterizations of linear differentiable operators, due to Peetre and Hormander. The inequalities of Garding and of Friedrichs on elliptic operators are proved and are used to prove the regularity of weak solutions of elliptic equations. The chapter ends with the approximation theorem of Malgrange-Lax and its application to the proof of the Runge theorem on open Riemann surfaces due to Behnke and Stein.
More details
Series
Edition
2nd edition
Language
English
Place of publication
United States
Publishing group
Elsevier Science & Technology
Target group
Professional and scholarly
Edition type
New edition
Product notice
Laminated cover
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 16 mm
Weight
548 gr
ISBN-13
978-0-444-87776-5 (9780444877765)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
R. Narasimhan
Analysis on Real and Complex Manifolds
E-Book
05/2014
2nd Edition
North-Holland
€54.95
Available for download
Content
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 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? Coefficients: The Regularity Theorem. Elliptic Operators with Analytic Coefficients. The Finiteness Theorem. The Approximation Theorem and Its Application to Open Riemann Surfaces