3 papers
math.AP2026
The Lp centro-sectional Minkowski problem
Karoly J. Boroczky, Jiaqian Liu, Renqing You
As part of Lutwak's broadening of the Brunn-Minkowski theory, and extending the notion of affine quermassintegrals and dual curvature measure discussed by Milman, Yehudayoff and Hu…
math.FA2025
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…
math.AP2024
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…