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arXiv · 1304.6308

Convex bodies with pinched Mahler volume under the centro-affine normal flows

Mohammad N. Ivaki
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Abstract

We study the asymptotic behavior of smooth, origin-symmetric, strictly convex bodies under the centro-affine normal flows. By means of a stability version of the Blaschke-Santal\'{o} inequality, we obtain regularity of the solutions provided that initial convex bodies have almost maximum Mahler volume. We prove that suitably rescaled solutions converge sequentially to the unit ball in the $\mathcal{C}^{\infty}$ topology modulo $SL(n+1)$.

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Mohammad N. Ivaki. 2013-04-23. Convex bodies with pinched Mahler volume under the centro-affine normal flows. https://arxiv.org/abs/1304.6308

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