Convex Integration Theory: Solutions to the H-Principle in Geometry and Topology

Voorkant
Springer, 1998 - 212 pagina's
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This book provides a comprehensive study of convex integration theory in immersion-theoretic topology. Convex integration theory, developed originally by M. Gromov, provides general topological methods for solving the h-principle for a wide variety of problems in differential geometry and topology, with applications also to PDE theory and to optimal control theory. Though topological in nature, the theory is based on a precise analytical approximation result for higher order derivatives of functions, proved by M. Gromov. This book is the first to present an exacting record and exposition of all of the basic concepts and technical results of convex integration theory in higher order jet spaces, including the theory of iterated convex hull extensions and the theory of relative h-principles. A second feature of the book is its detailed presentation of applications of the general theory to topics in symplectic topology, divergence free vector fields on 3-manifolds, isometric immersions, totally real embeddings, underdetermined non-linear systems of PDEs, the relaxation theorem in optimal control theory, as well as applications to the traditional immersion-theoretical topics such as immersions, submersions, k-mersions and free maps. The book should prove useful to graduate students and to researchers in topology, PDE theory and optimal control theory who wish to understand the h-principle and how it can be applied to solve problems in their respective disciplines.
  

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On the regularity of solution in Convex Integration theory
Invent. math. 104, 165 178 (1991). Inventiones. mathematicae. 9 Springer-Verlag 1991. On the regularity of solutions in Convex. Integration theory ...
www.springerlink.com/ index/ NT81282L18060W16.pdf

Mathematisches Forschungsinstitut Oberwolfach Arbeitsgemeinschaft ...
Mathematisches Forschungsinstitut Oberwolfach. Report No. 15/2003. Arbeitsgemeinschaft mit aktuellem Thema:. Convex Integration. March 30th – April 5th, ...
www.mfo.de/ programme/ schedule/ 2003/ 14/ Report15_2003.pdf

arxiv:math/0307127v1 [math.GT] 9 Jul 2003
THE GOLDEN AGE OF IMMERSION. THEORY IN TOPOLOGY: 1959-1973. David Spring. 1. Brief Overview. In this article* I briefly review selected contributions to ...
arxiv.org/ pdf/ math.GT/ 0307127.pdf

Convex integration theory : - / 1998 - Livros
Convex integration theory : solutions to the h-principle in geometry and topology . Basel ;: Boston: Birkhäuser, c1998. 212 p. ISBN 376435805X (Basel : acid ...
volterra.impa.br/ arquivos/ 25000/ 29300/ 105_29340.htm

livre convex integration theory : solutions to the h-principle in ...
Convex integration theory : solutions to the h-principle in geometry and topology. Auteur(s) : SPRING Date de parution: 01-1998 Langue : ANGLAIS ...
www.lavoisier.fr/ notice/ fr060203.html

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