Geometric Integration Theory

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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Krantz, Steven G. (Autor), Parks, Harold R. (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2008.
Edición:1st ed. 2008.
Colección:Cornerstones,
Temas:
Geometry.
Geometry, Differential.
Measure theory.
Integral equations.
Mathematical analysis.
Convex geometry .
Discrete geometry.
Differential Geometry.
Measure and Integration.
Integral Equations.
Integral Transforms and Operational Calculus.
Convex and Discrete Geometry.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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