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

  • Mohammad N. IvakiEmail author


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–Santaló 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 \(SL(n+1)\).

Mathematics Subject Classification

Primary 53C44 52A05 Secondary 35K55 



I am indebted to the referees whose comments and suggestions have led to improvements of this article.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institut für Diskrete Mathematik und GeometrieTechnische Universität WienWienAustria

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