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OPTIMAL SMOOTHING FOR CONVEX POLYTOPES

Published online by Cambridge University Press:  14 June 2004

MOHAMMAD GHOMI
MOHAMMAD GHOMI
Affiliation:
School of Mathematics, Georgia Institute of Technology, Atlanta GA 30332, USAghomi@math.gatech.edu
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Abstract

It is proved that, given a convex polytope $P$ in $\mathbb{R}^n$, together with a collection of compact convex subsets in the interior of each facet of $P$, there exists a smooth convex body arbitrarily close to $P$ that coincides with each facet precisely along the prescribed sets, and has positive curvature elsewhere.

Keywords

53A0752B1153C45
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 4 , July 2004 , pp. 483 - 492
Copyright
© The London Mathematical Society 2004

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