Title: On the stability of the $p$-affine isoperimetric inequality
Abstract: Employing the affine normal flow, we prove a stability version of the $p$-affine isoperimetric inequality for $p\geq1$ in $\mathbb{R}^2$ in the class of origin-symmetric convex bodies. That is, if $K$ is an origin-symmetric convex body in $\mathbb{R}^2$ such that it has area $\pi$ and its $p$-affine perimeter is close enough to the one of an ellipse with the same area, then, after applying a special linear transformation, $K$ is close to an ellipse in the Hausdorff distance.
Publication Year: 2012
Publication Date: 2012-09-30
Language: en
Type: preprint
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Cited By Count: 1
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