# Geometric Measure Theory Books

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## Geometric Measure Theory

- Author : Herbert Federer
- Publisher : Springer
- Release : 2014-11-25
- ISBN : 9783642620102
- Language : En, Es, Fr & De

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"This book is a major treatise in mathematics and is essential in the working library of the modern analyst." (Bulletin of the London Mathematical Society)

## Geometric Measure Theory

- Author : Frank Morgan
- Publisher : Elsevier
- Release : 2014-05-10
- ISBN : 9781483277806
- Language : En, Es, Fr & De

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Geometric Measure Theory: A Beginner's Guide provides information pertinent to the development of geometric measure theory. This book presents a few fundamental arguments and a superficial discussion of the regularity theory. Organized into 12 chapters, this book begins with an overview of the purpose and fundamental concepts of geometric measure theory. This text then provides the measure-theoretic foundation, including the definition of Hausdorff measure and covering theory. Other chapters consider the m-dimensional surfaces of geometric measure theory called rectifiable sets and introduce the two basic tools of the regularity theory of area-minimizing surfaces. This book discusses as well the fundamental theorem of geometric measure theory, which guarantees solutions to a wide class of variational problems in general dimensions. The final chapter deals with the basic methods of geometry and analysis in a generality that embraces manifold applications. This book is a valuable resource for graduate students, mathematicians, and research workers.

## Geometric Measure Theory

- Author : Frank Morgan
- Publisher : Academic Press
- Release : 2016-05-02
- ISBN : 9780128045275
- Language : En, Es, Fr & De

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Geometric Measure Theory: A Beginner's Guide, Fifth Edition provides the framework readers need to understand the structure of a crystal, a soap bubble cluster, or a universe. The book is essential to any student who wants to learn geometric measure theory, and will appeal to researchers and mathematicians working in the field. Brevity, clarity, and scope make this classic book an excellent introduction to more complex ideas from geometric measure theory and the calculus of variations for beginning graduate students and researchers. Morgan emphasizes geometry over proofs and technicalities, providing a fast and efficient insight into many aspects of the subject, with new coverage to this edition including topical coverage of the Log Convex Density Conjecture, a major new theorem at the center of an area of mathematics that has exploded since its appearance in Perelman's proof of the Poincaré conjecture, and new topical coverage of manifolds taking into account all recent research advances in theory and applications. Focuses on core geometry rather than proofs, paving the way to fast and efficient insight into an extremely complex topic in geometric structures Enables further study of more advanced topics and texts Demonstrates in the simplest possible way how to relate concepts of geometric analysis by way of algebraic or topological techniques Contains full topical coverage of The Log-Convex Density Conjecture Comprehensively updated throughout

## Lectures on Geometric Measure Theory

- Author : Leon Simon
- Publisher :
- Release : 1984
- ISBN : 0867844299
- Language : En, Es, Fr & De

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## Geometric Integration Theory

- Author : Steven G. Krantz
- Publisher : Springer Science & Business Media
- Release : 2008-12-15
- ISBN : 0817646795
- Language : En, Es, Fr & De

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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.