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: Geometric Integration Theory
  name:
    name part: Krantz, Steven.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Parks, Harold.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2008
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 340 p. 33 illus. online resource.
  abstract: This textbook introduces geometric measure theory through the notion of currents. Currents—continuous linear functionals on spaces of differential forms—are a natural language in which to formulate various types of extremal problems arising in geometry, and can be used to study generalized versions of the Plateau problem and related questions in geometric analysis. Key features of Geometric Integration Theory: * Includes topics on the deformation theorem, the area and coarea formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces * Applies techniques to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics * Provides considerable background material for the student Motivating key ideas with examples and figures, Geometric Integration Theory is a comprehensive introduction ideal for use in the classroom and for self-study. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for graduate students and researchers.
  table of contents: Basics -- Carathéodory’s Construction and Lower-Dimensional Measures -- Invariant Measures and the Construction of Haar Measure. -- Covering Theorems and the Differentiation of Integrals -- Analytical Tools: The Area Formula, the Coarea Formula, and Poincaré Inequalities. -- The Calculus of Differential Forms and Stokes’s Theorem -- to Currents -- Currents and the Calculus of Variations -- Regularity of Mass-Minimizing Currents.
  note: by Steven Krantz, Harold Parks.
  subject:
    topic: Mathematics
  subject:
    topic: Integral equations
  subject:
    topic: Integral transforms
  subject:
    topic: Operational calculus
  subject:
    topic: Measure theory
  subject:
    topic: Geometry
  subject:
    topic: Convex geometry
  subject:
    topic: Discrete geometry
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematics
  subject:
    topic: Geometry
  subject:
    topic: Differential Geometry
  subject:
    topic: Measure and Integration
  subject:
    topic: Integral Equations
  subject:
    topic: Integral Transforms, Operational Calculus
  subject:
    topic: Convex and Discrete Geometry
  classification: QA440-699
  classification: 516
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Cornerstones
  identifier: 9780817646790
  identifier: http://dx.doi.org/10.1007/978-0-8176-4679-0
  record info:
    record creation date: 100301
    record change date: 20151204160400.0
    record identifier: 978-0-8176-4679-0