Introduction To The H Principle
Download and Read Introduction To The H Principle full books in PDF, ePUB, and Kindle. Read online free Introduction To The H Principle ebook anywhere anytime directly on your device. We cannot guarantee that every ebooks is available!
Introduction to the $h$-Principle
Author | : K. Cieliebak |
Publisher | : American Mathematical Society |
Total Pages | : 384 |
Release | : 2024-01-30 |
Genre | : Mathematics |
ISBN | : 1470476177 |
Download Introduction to the $h$-Principle Book in PDF, Epub and Kindle
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 1950s 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 is made on applications to symplectic and contact geometry. The present book is the first broadly accessible exposition of the theory and its applications, making it 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. This second edition of the book is significantly revised and expanded to almost twice of the original size. The most significant addition to the original book is the new part devoted to the method of wrinkling and its applications. Several other chapters (e.g., on multivalued holonomic approximation and foliations) are either added or completely rewritten.
Introduction to the $h$-Principle Related Books
Pages: 226
Pages: 226
Pages: 384
Pages: 219
Pages: 0