Cornerstones

Geometric Integration Theory

Authors: Krantz, Steven G, Parks, Harold R.

  • 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
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eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-4679-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-0-8176-4676-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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 of the Plateau problem and related questions in geometric analysis.

Key features of Geometric Integration Theory:

* Includes topics on the deformation theorem, the area and coarea formulas, the compactness theorem, the slicing theorem and applications to minimal surfaces

* Applies techniques to complex geometry, partial differential equations, harmonic analysis, differential geometry, and many other parts of mathematics

* Provides considerable background material for the student

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

Reviews

From the reviews:

"This is a graduate textbook with the main purpose of introducing geometric measure theory through the notion of currents. … One of the most important features of this text is that it is self-contained … . The book also contains an Appendix … as well as extended list of references, making it a good text for a graduate course, as well as for an independent or self study." (Mihaela Poplicher, The Mathematical Association of America, March, 2009)

"The book under review succeeds in giving a complete and readable introduction to geometric measure theory. It can be used by students willing to learn this beautiful theory or by teachers as a basis for a one- or two-semester course." (Andreas Bernig, Mathematical Reviews, Issue 2009 m)

“The authors present main fields of applications, namely the isoperimetric problem and the regularity of minimal currents. The exposition is detailed and very well organized and therefore the book should be quite accessible for graduate students.” (R. Steinbauer, Monatshefte für Mathematik, Vol. 162 (3), March, 2011)


Table of contents (10 chapters)

Buy this book

eBook $59.99
price for USA (gross)
  • ISBN 978-0-8176-4679-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $79.99
price for USA
  • ISBN 978-0-8176-4676-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometric Integration Theory
Authors
Series Title
Cornerstones
Copyright
2008
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Boston
eBook ISBN
978-0-8176-4679-0
DOI
10.1007/978-0-8176-4679-0
Hardcover ISBN
978-0-8176-4676-9
Series ISSN
2197-182X
Edition Number
1
Number of Pages
XVI, 340
Number of Illustrations and Tables
33 b/w illustrations
Topics