Convex sets with homothetic projections

Details Convex sets with homothetic projections Convex sets with homothetic projections

2009-03-16

arxiv.org/abs/0903.2836v1

Mathematics

Metric Geometry

13 pages

Scientific paper

Extending 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.

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