Introduction to the $h$-Principle

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9780821832271: Introduction to the $h$-Principle
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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.

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Book by Eliashberg Y Mishachev N

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Y. Eliashberg, N. Mishachev
Editore: American Mathematical Society, United States (2002)
ISBN 10: 0821832271 ISBN 13: 9780821832271
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Descrizione libro American Mathematical Society, United States, 2002. Hardback. Condizione: New. Language: English . Brand New Book. 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. Codice articolo AAN9780821832271

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Descrizione libro American Mathematical Society. Hardback. Condizione: New. New copy - Usually dispatched within 2 working days. Codice articolo B9780821832271

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N. Mishachev, Y. Eliashberg
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ISBN 10: 0821832271 ISBN 13: 9780821832271
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Descrizione libro American Mathematical Society, United States, 2002. Hardback. Condizione: New. Language: English. Brand new Book. 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. Codice articolo AAN9780821832271

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Descrizione libro Amer Mathematical Society, 2002. Hardcover. Condizione: Brand New. 206 pages. 10.00x7.00x0.75 inches. In Stock. Codice articolo __0821832271

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Descrizione libro Amer Mathematical Society, 2002. Condizione: New. book. Codice articolo M0821832271

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Descrizione libro Amer Mathematical Society. Hardcover. Condizione: New. 0821832271 New Condition. Codice articolo NEW7.0420809

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