On \(L_{p}\)-affine surface area and curvature measures (Q2800173)
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scientific article; zbMATH DE number 6569169
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(L_{p}\)-affine surface area and curvature measures |
scientific article; zbMATH DE number 6569169 |
Statements
15 April 2016
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affine surface area
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curvature measures
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affine isoperimetric inequality
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upper semi-continuity
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On \(L_{p}\)-affine surface area and curvature measures (English)
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A new definition of \(L_p\)-affine surface area (Definition 1.5, Theorem 1.6, Definition 3.1) is given, it depends only on curvature measures. Its equivalence to older definitions is established. Important properties, such as upper semi-continuity and affine isoperimetric inequality are proven somewhat easier than for other definitions. A good survey of this area of research is given in the introduction section of this paper.
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