書誌事項

Geometric integration theory

Steven G. Krantz, Harold R. Parks

(Cornerstones)

Birkhäuser, c2008

大学図書館所蔵 件 / 全28件

この図書・雑誌をさがす

注記

Includes bibliographical references (p. [323]-327) and indexes

内容説明・目次

内容説明

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.

目次

Basics.- Caratheodory'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 Poincare Inequalities..- The Calculus of Differential Forms and Stokes's Theorem.- to Currents.- Currents and the Calculus of Variations.- Regularity of Mass-Minimizing Currents.

「Nielsen BookData」 より

関連文献: 1件中  1-1を表示

詳細情報

ページトップへ

AltStyle によって変換されたページ (->オリジナル) /