https://neckpinch.com/authors/kwok-kun-kwong/New arXiv papers by Kwok-Kun Kwong, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2503.15884/arxiv:2503.15884Thu, 20 Mar 2025 00:00:00 GMTKwok-Kun Kwong, Yong Wei — We derive a number of sharp upper bounds for the deficit in the Alexandrov-Fenchel inequality using a weighted Minkowski integral formula and an integral formula for the deficit in Jensen's inequality. Our estimates yield results under weaker convexity assumptions compared to approaches based on inverse curvature flows. The use of weighted formulas provides flexibility in deriving inequalities with different weight functions. Furthermore, our estimates are more quantitative as they include a distance term measuring the domain's deviation from a reference ball. We also analyze the stability of a weighted geometric inequality from a recent paper via analysis of the support function on the sphere and show that, with an optimal choice of the origin, this inequality is stronger than the classical isoperimetric inequality.Other curvature flowsInverse mean curvature flowStability & uniquenessGeometric inequalities