OPTIMAL SMOOTHING FOR CONVEX POLYTOPES

It is proved that, given a convex polytope P in Rn, 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 elsewhe...

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Bibliographic Details
Published inThe Bulletin of the London Mathematical Society Vol. 36; no. 4; pp. 483 - 492
Main Author GHOMI, MOHAMMAD
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.07.2004
Oxford University Press
Subjects
53C45
53A07
52B11
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ISSN0024-6093
1469-2120
DOI10.1112/S0024609303003059

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Summary:It is proved that, given a convex polytope P in Rn, 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. 2000 Mathematics Subject Classification 53A07, 52B11, 53C45.
Bibliography:ark:/67375/HXZ-W35NMML4-5
ArticleID:36.4.483
The author was partially supported by the NSF grant DMS-0204190, and CAREER award DMS-0332333.
istex:750E3BFA1141535697A7A2220D51ED36FDE3D55C
The author was partially supported by the NSF grant DMS‐0204190, and CAREER award DMS‐0332333.
ISSN:0024-6093
1469-2120
DOI:10.1112/S0024609303003059