6 papers
From Cauchy to Gaussian: Sharp Lower Deviations and Ehrhard-Type Inequality
Yong Huang, Shengyu Tang, Sinan Wang
We establish dimension-free, pointwise optimal lower-deviation bounds for convex functions under spherically symmetric Cauchy-type measures. These bounds use either mean-variance n…
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…
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. In…
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…
The Generalized Gaussian Minkowski Problem
Jiaqian Liu, Shengyu Tang
This article delves into the Minkowski problem within the framework of generalized Gaussian probability space. This type of probability space was initially introduced in info…