2020/10/19 by Dmitry Ryabogin, Ryabogin, Dmitry
Mathematics · #52Axx #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.MG #msc:52Axx
paper · pdf · doi:10.48550/arxiv.2010.09864
9 figures, 20 pages
openalex publication_date 2020/10/19 · arxiv created 2021/11/09 · arxiv updated 2021/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let d≥ 2 and let K and L be two convex bodies in \mathbb Rd such that L⊂ \textrmint K and the boundary of L does not contain a segment. If K and L satisfy the (d+1)-equichordal property, i.e., for any line l supporting the boundary of L and the points \ζ±\ of the intersection of the boundary of K with l, \textrmdistd+1(L∩ l, ζ+)+\textrmdistd+1(L∩ l, ζ-)=2σd+1 holds, where the constant σ is independent of l, does it follow that K and L are concentric Euclidean balls? We prove that if K and L have C2-smooth boundaries and L is a body of revolution, then K and L are concentric Euclidean balls.