Convex sets with homothetic projections

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dc.creatorSoltan, V.
dc.date2009-03-16
dc.date.accessioned2026-07-07T12:52:57Z
dc.date.available2026-07-07T12:52:57Z
dc.descriptionExtending results of Suss and Hadwiger (proved by them for the case of convex bodies and positive ratios), we show that compact (respectively, closed) convex sets in the Euclidean space of dimension n are homothetic provided for any given integer m between 2 and n - 1 (respectively, between 3 and n - 1), the orthogonal projections of the sets on every m-dimensional plane are homothetic, where homothety ratio and its sign may depend on the projection plane. The proof uses a refined version of Straszewicz's theorem on exposed points of compact convex sets.
dc.description13 pages
dc.identifierhttps://arxiv.org/abs/0903.2836
dc.identifierhttp://arxiv.org/abs/0903.2836
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/223462
dc.subjectMetric Geometry
dc.subject52A20
dc.titleConvex sets with homothetic projections
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