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THE FLOATING BODY PROBLEM

Published online by Cambridge University Press:  20 September 2006

A. STANCU
A. STANCU
Affiliation:
Department of Mathematics, Polytechnic University of New York, Brooklyn, NY 11201, USAastancu@duke.poly.edu Département des Mathématiques et de Statistique, Université de Montréal, Montréal, QC, H3C 3J7, Canadastancu@dms.umontreal.ca
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Abstract

Let $K$ be a convex body with boundary of class ${\mathcal{C}}^{\geq 4}$. We prove that, for a sufficiently small $\delta$, the floating body $K_{\delta}$ is homothetic to $K$ if and only if $K$ is an ellipsoid. The proof relies on properties of the affine curvature flow.

Keywords

52A20 (primary)52A38 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 5 , October 2006 , pp. 839 - 846
Copyright
© The London Mathematical Society 2006

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