4 papers
Brunn-Minkowski inequality for weighted dual quermassintegrals
Xiaojuan Chen, Shengyu Tang, Sinan Wang
We investigate the Brunn-Minkowski inequality for dual quermassintegrals in weighted measure spaces, which is a special class of rotationally invariant measures proposed by C…
Minkowski problem and Brunn-Minkowski inequality for dual quermassintegrals
Xiaojuan Chen, Shengyu Tang, Sinan Wang
This paper studies the core problems in the dual Brunn-Minkowski theory, encompassing the Minkowski problem and Brunn-Minkowski inequality for dual quermassintegr…
The Weighted Minkowski Problem
Dylan Langharst, Jiaqian Liu, Shengyu Tang
The Minkowski problem in convex geometry concerns showing that a given Borel measure on the unit sphere is, up to perhaps a constant, some type of surface area measure of a convex…
Grünbaum's inequality for Gaussian and convex probability measures
Matthieu Fradelizi, Dylan Langharst, Jiaqian Liu +2
A celebrated result in convex geometry is Grünbaum's inequality, which quantifies how much volume of a convex body can be cut off by a hyperplane passing through its barycenter. I…