Geometric Integration Theory

This self-contained and accessible textbook introduces geometric measure theory through the notion of currents. Motivating key ideas with examples and figures, this book is a comprehensive introduction ideal for both self-study and for use in the classroom.

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, Geometric Integration Theory 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.

Self-contained, inclusive, and accessible for both the graduate students and researchers Motivates the key ideas with examples and figures Includes considerable background material and complete proofs

Auteur
Steven Krantz, Ph.D., is Chairman of the Mathematics Department at Washington University in St. Louis. An award-winning teacher and author, Dr. Krantz has written more than 45 books on mathematics, including Calculus Demystified, another popular title in this series. He lives in St. Louis, Missouri.

Contenu
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.