2024/10/07 by Letwin, Brayden, Yaskin, Vladyslav · 2 citations
#52A20 (Primary) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2410.04741
Grünbaum's inequality gives sharp bounds between the volume of a convex body and its part cut off by a hyperplane through the centroid of the body. We provide a generalization of this inequality for hyperplanes that do not necessarily contain the centroid. As an application, we obtain a sharp inequality that compares sections of a convex body to the maximal section parallel to it.