Geometric Integration Theory

• Main Authors: Krantz, Steven (Author), Parks, Harold (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston : Birkhäuser Boston, 2008.
• Series: Cornerstones
• Subjects: Mathematics.; Integral equations.; Integral transforms.; Operational calculus.; Measure theory.; Geometry.; Convex geometry.; Discrete geometry.; Differential geometry.; Differential Geometry.; Measure and Integration.; Integral Equations.; Integral Transforms, Operational Calculus.; Convex and Discrete Geometry.

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...

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.