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Analysis on Real and Complex Manifolds Raghavan Narasimhan

Analysis on Real and Complex Manifolds

Raghavan Narasimhan

Published December 15th 1985
ISBN : 9780444877765
Hardcover
245 pages
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 About the Book 

Chapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sards theorem and Whitneys approximation theorem.The next chapter is an introduction to real and complex manifolds.MoreChapter 1 presents theorems on differentiable functions often used in differential topology, such as the implicit function theorem, Sards theorem and Whitneys 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 Grothendiecks lemma to complex analysis, the imbedding theorem of Whitney and Thoms 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.