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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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Main Authors: Krantz, Steven G. (Author, http://id.loc.gov/vocabulary/relators/aut), Parks, Harold R. (http://id.loc.gov/vocabulary/relators/aut)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2008.
Edition:1st ed. 2008.
Series:Cornerstones,
Subjects:
Geometry.
Differential geometry.
Measure theory.
Integral equations.
Integral transforms.
Operational calculus.
Convex geometry .
Discrete geometry.
Differential Geometry.
Measure and Integration.
Integral Equations.
Integral Transforms, Operational Calculus.
Convex and Discrete Geometry.
Online Access:https://doi.org/10.1007/978-0-8176-4679-0
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.

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