2024/07/17 by E. Morales‐Amaya, Morales-Amaya, Efren
Mathematics · #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2407.12310
In this work we present a theorem regarding two convex bodies K1, K2⊂ ℝn, n≥ 3, and two families of sections of them, given by two families of tangent planes of two spheres Si⊂ \textrmint\textrm Ki, i=1,2 such that, for every pair Π1, Π2 of parallel supporting planes of S1, S2, respectively, which are corresponding (this means, that the outer normal vectors of the supporting half spaces determined by the two planes have the same direction), the sections Π1∩ K1, Π2∩ K2 are translated, the theorem claims that if S1, S2 have the same radius, the bodies are translated, otherwise, the bodies are also spheres.