2020/10/18 by Dan I. Florentin, Carsten Schuett, Florentin, D. I. +5
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematics and Applications #Metric Geometry (math.MG) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2010.09006
openalex publication_date 2020/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study a long standing open problem by Ulam, which is whether the Euclidean ball is the unique body of uniform density which will float in equilibrium in any direction. We answer this problem in the class of origin symmetric n-dimensional convex bodies whose relative density to water is 1/2. For n=3, this result is due to Falconer.