Centro-affine invariants for smooth convex bodies (Q2889567)
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scientific article; zbMATH DE number 6043644
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Centro-affine invariants for smooth convex bodies |
scientific article; zbMATH DE number 6043644 |
Statements
8 June 2012
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smooth convex bodies
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centro-affine flow
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centro-affine invariants
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isoperimetric inequality
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\(L_{\phi }\) affine surface area
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Centro-affine invariants for smooth convex bodies (English)
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This paper starts with the definition of the centro-affine flow and several of its properties. Then the author recalls the definition of \(L_{p}\) affine surface areas, \(\Omega_{p}\), and list several inequalities for them implied by the flow. The fourth section states the main result defining the new centro-affine invariants and proves a sharp isoperimetric inequality for a class of such invariants. In the last section, the author shows a geometric interpretation of the \(L_{\phi }\) affine surface area introduced by Ludwig and Reitzner.
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