2026/06/30 by Wang Shouda, Xiong Ge, Yang Kaiwen
Mathematics · #math.MG #msc:52A20 #msc:33C55 #msc:57R70
18 pages, 1 figure. This version has three authors. The results in this paper are obtained independently and simultaneously by Shouda Wang (at Princeton University) and by Ge Xiong and Kaiwen Yang (at Tongji University)
arxiv created 2026/07/31 · arxiv updated 2026/08/03
In the 1960s, Grünbaum and Loewner raised problems concerning the minimum possible number of hyperplane sections of a convex body in Rn whose centroids coincide with the centroid of the body itself. By employing the hemispherical transform and Morse theory, we provide a complete solution to these problems.