Ulam Floating Body

2018/03/22 by Huang, Han, Slomka, Boaz A., Werner, Elisabeth M. · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1803.08224

Abstract

We study a new construction of bodies from a given convex body in ℝⁿ which are isomorphic to (weighted) floating bodies. We establish several properties of this new construction, including its relation to p-affine surface areas. We show that these bodies are related to Ulam's long-standing floating body problem which asks whether Euclidean balls are the only bodies that can float, without turning, in any orientation.

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