\(L_p\) mixed geominimal surface area (Q465219)
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scientific article; zbMATH DE number 6362874
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(L_p\) mixed geominimal surface area |
scientific article; zbMATH DE number 6362874 |
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\(L_p\) mixed geominimal surface area (English)
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31 October 2014
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Some integral representations and inequalities are derived for the \(L_{p}\) geominimal surface area. Extensions of this concept are introduced, called \(L_{p}\) mixed geominimal surface area and the \(i\)th \(L_{p}\) mixed geominimal surface area. More inequalities are derived for the new functions: an analogue of Alexandrov-Fenchel inequality, affine isoperimetric inequality, cyclic inequality, Minkowski type inequality, Blasche-Santaló inequality, the generalized isoperimetric inequality. All the inequalities are sharp.
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\(L_{p}\) geominimal surface area
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\(L_{p}\) mixed geominimal surface area
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\(L_{p}\) affine surface area
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affine isoperimetric inequality
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