Introduction to the H-Principle - Rilegato

Eliashberg, Y.; Mishachev, N.

Rilegato

ISBN 10: 0821832271 ISBN 13: 9780821832271

Casa editrice: Amer Mathematical Society, 2002

Riassunto

One of the most powerful modern methods of solving partial differential equations is Gromov's $h$-principle. It has also been, traditionally, one of the most difficult to explain. This book is the first broadly accessible exposition of the principle and its applications. The essence of the $h$-principle is the reduction of problems involving partial differential relations to problems of a purely homotopy-theoretic nature. Two famous examples of the $h$-principle are the Nash-Kuiper $C1$-isometric embedding theory in Riemannian geometry and the Smale-Hirsch immersion theory in differential topology. Gromov transformed these examples into a powerful general method for proving the $h$-principle. Both of these examples and their explanations in terms of the $h$-principle are covered in detail in the book. The authors cover two main embodiments of the principle: holonomic approximation and convex integration. The first is a version of the method of continuous sheaves. The reader will find that, with a few notable exceptions, most instances of the $h$-principle can be treated by the methods considered here. There are, naturally, many connections to symplectic and contact geometry. The book would be an excellent text for a graduate course on modern methods for solving partial differential equations. Geometers and analysts will also find much value in this very readable exposition of an important and remarkable technique.

Su questo libro

Product Description:

Book by Eliashberg Y Mishachev N

Su questa edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2002
• ISBN 10: 0821832271
• ISBN 13: 9780821832271
• Rilegatura: Copertina rigida
• Numero di pagine: 206