Geometric measure theory

Herbert Federer

"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)

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[目次]

  • 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

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この本の情報

書名 Geometric measure theory
著作者等 Federer, Herbert
シリーズ名 Classics in mathematics
出版元 Springer
刊行年月 c1996
ページ数 xiv, 676 p.
大きさ 24 cm
ISBN 3540606564
NCID BA26845809
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言語 英語
出版国 ドイツ
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