Overview

"From the reviews: ""...Federer's timely and beautiful book indeed fills the need for a comprehensive treatise on geometric measure theory, and his detailed exposition leads from the foundations of the theory to the most recent discoveries...The author writes with a distinctive style which is both natural and powerfully economical in treating a complicated subject. 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"

Full Product Details

Author:   Herbert Federer
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Reprint of the 1st ed. Berlin, Heidelberg, New York 1969
Volume:   153
Dimensions:   Width: 15.50cm , Height: 3.50cm , Length: 23.50cm
Weight:   2.130kg
ISBN:  

9783540606567

ISBN 10:   3540606564
Pages:   677
Publication Date:   05 January 1996
Audience:   Professional and scholarly ,  Professional and scholarly ,  Professional & Vocational ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

Introduction Chapter 1 Grassmann algebra 1.1 Tensor products 1.2 Graded algebras 1.3 Teh exterior algebra of a vectorspace 1.4 Alternating forms and duality 1.5 Interior multiplications 1.6 Simple m-vectors 1.8 Mass and comass 1.9 The symmetric algebra of a vectorspace 1.10 Symmetric forms and polynomial functions Chapter 2 General measure theory 2.1 Measures and measurable sets 2.2 Borrel and Suslin sets 2.3 Measurable functions 2.4 Lebesgue integrations 2.5 Linear functionals 2.6 Product measures 2.7 Invariant measures 2.8 Covering theorems 2.9 Derivates 2.10 Caratheodory's construction Chapter 3 Rectifiability 3.1 Differentials and tangents 3.2 Area and coarea of Lipschitzian maps 3.3 Structure theory 3.4 Some properties of highly differentiable functions Chapter 4 Homological integration theory 4.1 Differential forms and currents 4.2 Deformations and compactness 4.3 Slicing 4.4 Homology groups 4.5 Normal currents of dimension n in R(-63) superscript n Chapter 5 Applications to thecalculus of variations 5.1 Integrands and minimizing currents 5.2 Regularity of solutions of certain differential equations 5.3 Excess and smoothness 5.4 Further results on area minimizing currents Bibliography Glossary of some standard notations List of basic notations defined in the text Index

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Author Information

Biography of Herbert Federer Herbert Federer was born on July 23, 1920, in Vienna. After emigrating to the US in 1938, he studied mathematics and physics at the University of California, Berkeley. Affiliated to Brown University, Providence since 1945, he is now Professor Emeritus there. The major part of Professor Federer's scientific effort has been directed to the development of the subject of Geometric Measure Theory, with its roots and applications in classical geometry and analysis, yet in the functorial spirit of modern topology and algebra. His work includes more than thirty research papers published between 1943 and 1986, as well as this book.

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