Introduction to the H-Principle (Graduate Studies in Mathematics, V 48)

Eliashberg, Y. and N. Mishachev:

ISBN 10: 0821832271 / ISBN 13: 9780821832271

Published by American Mathematical Society., 2002

About this Item

206 Seiten, mit Abbildungen, Zust: Gutes Exemplar. Schneller Versand und persönlicher Service - jedes Buch händisch geprüft und beschrieben - aus unserem Familienbetrieb seit über 25 Jahren. Eine Rechnung mit ausgewiesener Mehrwertsteuer liegt jeder unserer Lieferungen bei. Wir versenden mit der deutschen Post. Sprache: Englisch Gewicht in Gramm: 6063.

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Bibliographic Details

• Title: Introduction to the H-Principle (Graduate Studies in Mathematics, V 48)
• Publisher: American Mathematical Society.
• Publication Date: 2002
• Language: English
• ISBN 10: 0821832271
• ISBN 13: 9780821832271
• Binding: Karton Karton
• Condition: Sehr gut
• Weight: 6063 grams
• Seller catalogs:
  • Mathematik

About this title

Synopsis

In differential geometry and topology one often deals with systems of partial differential equations, as well as partial differential inequalities, that have infinitely many solutions whatever boundary conditions are imposed. It was discovered in the fifties that the solvability of differential relations (i.e. equations and inequalities) of this kind can often be reduced to a problem of a purely homotopy-theoretic nature. One says in this case that the corresponding differential relation satisfies the $h$-principle. Two famous examples of the $h$-principle, the Nash-Kuiper $C^1$-isometric embedding theory in Riemannian geometry and the Smale-Hirsch immersion theory in differential topology, were later transformed by Gromov into powerful general methods for establishing the $h$-principle.

The authors cover two main methods for proving the $h$-principle: holonomic approximation and convex integration. The reader will find that, with a few notable exceptions, most instances of the $h$-principle can be treated by the methods considered here. A special emphasis in the book is made on applications to symplectic and contact geometry.

Gromov's famous book "Partial Differential Relations", which is devoted to the same subject, is an encyclopedia of the $h$-principle, written for experts, while the present book is the first broadly accessible exposition of the theory and its applications. The book would be an excellent text for a graduate course on geometric methods for solving partial differential equations and inequalities. Geometers, topologists and analysts will also find much value in this very readable exposition of an important and remarkable topic.