Analysis on Real and Complex Manifolds

✍ Scribed by R. Narasimhan (Eds.)

• Publisher: North Holland
• Year: 1985
• Leaves: 256
• Series: North-Holland Mathematical Library 35
• Edition: 2
• Category: Library

✦ Synopsis

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 Poincaré 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.

✦ Table of Contents

Content:
Edited by
Page iii

Copyright page
Page iv

Preface
Pages v-vi
Raghavan Narasimhan

Preface to the third printing
Pages vii-xii

Chapter 1 Differentiable functions in Rⁿ
Pages 1-51

Chapter 2 Manifolds
Pages 52-154

Chapter 3 Linear elliptic differential operators
Pages 155-241

References
Pages 242-244

Subject Index
Pages 245-246