rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Convex integration theory
    sub title: solutions to the h-principle in geometry and topology
  name:
    name part: Spring, David
    name part: 1939-
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: sz
    date issued: 1998
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: preservation
    reformatting quality: access
    form: remote
    extent: 1 online resource (viii, 212 pages) : illustrations.
  abstract: 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.
  table of contents: Convex Hulls -- Analytic Theory -- Open Ample Relations in 1-Jet Spaces -- Microfibrations -- The Geometry of Jet Spaces -- Convex Hull Extensions -- Ample Relations -- Systems of Partial Differential Equations -- Relaxation Theory.
  note: David Spring.
  note: Electronic resource.
  note: Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002. http://purl.oclc.org/DLF/benchrepro0212 MiAaHDL
  note: digitized 2011 HathiTrust Digital Library committed to preserve pda MiAaHDL
  note: Includes bibliographical references (pages 207-209) and indexes.
  subject:
    topic: Differential topology
  subject:
    topic: Differential topology
  subject:
    topic: Topologie différentielle
  subject:
    topic: Differentialtopologie
  classification: QA613.6 .S67 1998
  classification: 514/.72
  classification: MAT 285f
  classification: SK 350
  related item:
    identifier: (DLC) 97046762
    identifier: (OCoLC)38048134
  related item:
    title info:
      title: Monographs in mathematics ; v. 92
  identifier: 9783034889407 (electronic bk.)
  identifier: 3034889402 (electronic bk.)
  identifier: 9783034800600 (electronic bk.)
  identifier: 3034800606 (electronic bk.)
  identifier: 376435805X (Basel : acid-free paper)
  identifier: 9783764358051 (Basel : acid-free paper)
  identifier: 081765805X (Boston : acid-free paper)
  identifier: 9780817658052
  identifier: 9783034898362
  identifier: 3034898363
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OCLCE
    record creation date: 110818
    record change date: 20260422211801.8
    record identifier: in00003499942
    language of cataloging:
      language term: eng