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Viser: Geometric Measure Theory
Geometric Measure Theory
(2021)
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Detaljer om varen
- 1. Udgave
- Udgiver: (Oktober 2021)
- ISBN: 9783540606567
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
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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Tlf 77 42 43 44 - email poly@polyteknisk.dk - CVR 34072655 - Sydbank Reg: 6748 Konto 0001107927