Geometric Measure Theory

Classics in Mathematics

Herbert Federer

676 pages, parution le 15/04/2003

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Résumé

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

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 the calculus 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

L'auteur - Herbert Federer

Brown University, Providence, RI, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Herbert Federer
Parution	15/04/2003
Nb. de pages	676
Format	15,5 x 23,5
Couverture	Broché
Poids	1030g
Intérieur	Noir et Blanc
EAN13	9783540606567