Alexandrov-Fenchel type inequalities with convex weight in space forms

Abstract

In this paper, we derive new sharp weighted Alexandrov-Fenchel and Minkowski inequalities for smooth, closed hypersurfaces under various convexity assumptions in Euclidean, spherical, and hyperbolic spaces. These inequalities extend classical results by incorporating weights given by convex, non-decreasing positive functions, which are otherwise arbitrary. Our approach gives rise to a broad family of geometric inequalities, as each convex, non-decreasing function yields a corresponding inequality, providing considerable flexibility.

21 pages

References in corpus (3)

• Locally constrained curvature flows and geometric inequalities in hyperbolic space
• A fully-nonlinear flow and quermassintegral inequalities in the sphere
• Geometric inequalities involving three quantities in warped product manifolds