Geometric Measure Theory
(Sprache: Englisch)
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Inhaltsverzeichnis zu „Geometric Measure Theory “
Introduction Chapter1 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
Chapter2 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
Chapter3 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
Chapter4 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
Chapter5 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.
Autoren-Porträt von 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.
Bibliographische Angaben
- Autor: Herbert Federer
- 1996, Repr. of the 1969 ed., 677 Seiten, Maße: 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer
- ISBN-10: 3540606564
- ISBN-13: 9783540606567
Sprache:
Englisch
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