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Author : Herbert Federer
Release : 2014-11-25
Genre : Mathematics
Kind : eBook
Book Rating : 108/5 ( reviews)
Book Synopsis Geometric Measure Theory by : Herbert Federer
Download or read book Geometric Measure Theory written by Herbert Federer. This book was released on 2014-11-25. Available in PDF, EPUB and Kindle. Book excerpt: "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)
Author : Frank Morgan
Release : 2014-05-10
Genre : Mathematics
Kind : eBook
Book Rating : 801/5 ( reviews)
Book Synopsis Geometric Measure Theory by : Frank Morgan
Download or read book Geometric Measure Theory written by Frank Morgan. This book was released on 2014-05-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Steven G. Krantz
Release : 2008-12-15
Genre : Mathematics
Kind : eBook
Book Rating : 795/5 ( reviews)
Book Synopsis Geometric Integration Theory by : Steven G. Krantz
Download or read book Geometric Integration Theory written by Steven G. Krantz. This book was released on 2008-12-15. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Francesco Maggi
Release : 2012-08-09
Genre : Mathematics
Kind : eBook
Book Rating : 891/5 ( reviews)
Book Synopsis Sets of Finite Perimeter and Geometric Variational Problems by : Francesco Maggi
Download or read book Sets of Finite Perimeter and Geometric Variational Problems written by Francesco Maggi. This book was released on 2012-08-09. Available in PDF, EPUB and Kindle. Book excerpt: The marriage of analytic power to geometric intuition drives many of today's mathematical advances, yet books that build the connection from an elementary level remain scarce. This engaging introduction to geometric measure theory bridges analysis and geometry, taking readers from basic theory to some of the most celebrated results in modern analysis. The theory of sets of finite perimeter provides a simple and effective framework. Topics covered include existence, regularity, analysis of singularities, characterization and symmetry results for minimizers in geometric variational problems, starting from the basics about Hausdorff measures in Euclidean spaces and ending with complete proofs of the regularity of area-minimizing hypersurfaces up to singular sets of codimension 8. Explanatory pictures, detailed proofs, exercises and remarks providing heuristic motivation and summarizing difficult arguments make this graduate-level textbook suitable for self-study and also a useful reference for researchers. Readers require only undergraduate analysis and basic measure theory.
Author : Leon Simon
Release : 1984
Genre : Geometric measure theory
Kind : eBook
Book Rating : 290/5 ( reviews)
Book Synopsis Lectures on Geometric Measure Theory by : Leon Simon
Download or read book Lectures on Geometric Measure Theory written by Leon Simon. This book was released on 1984. Available in PDF, EPUB and Kindle. Book excerpt:
