Geometric Integration Theory / Edition 1

Geometric Integration Theory / Edition 1

by Steven G Krantz, Harold R. Parks
     
 

ISBN-10: 0817646760

ISBN-13: 9780817646769

Pub. Date: 08/12/2008

Publisher: Birkhauser Verlag

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 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.

Overview

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 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. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom. The exposition demands minimal background, is self-contained and accessible, and thus is ideal for both graduate students and researchers.

Product Details

ISBN-13:
9780817646769
Publisher:
Birkhauser Verlag
Publication date:
08/12/2008
Series:
Cornerstones Series
Edition description:
2008
Pages:
340
Product dimensions:
6.30(w) x 9.30(h) x 0.90(d)

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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