4 papers · 1 filter
Volume and Projection Inequalities I: Zonoids and Courtade's Conjecture
Matthieu Fradelizi, Alfredo Hubard, Auttawich Manui +3
We study volume and projection inequalities for zonoids through the multiaffine determinant polynomials that encode their volumes. We show that a log-submodularity conjecture for t…
A complete solution to the Grünbaum--Loewner centroid problems
Xiong Ge, Wang Shouda, Yang Kai-Wen +1
In the 1960s, Grünbaum and Loewner raised problems concerning the minimum possible number of hyperplane sections of a convex body in whose centroids coincide with the centro…
Monotonicity of the deficit in the local log-Brunn-Minkowski inequality
Shouda Wang
We establish a monotonicity property of the deficit associated with the local log-Brunn-Minkowski inequality (LLBM) under addition of line segments. As a corollary, if the LLBM hol…
On Minkowski's monotonicity problem
Ramon van Handel, Shouda Wang
We address an old open question in convex geometry that dates back to the work of Minkowski: what are the equality cases of the monotonicity of mixed volumes? The problem is equiva…