Functional inequalities on manifolds with non-convex boundary

TL;DR

This paper introduces new curvature conditions to establish various functional inequalities on manifolds with non-convex boundaries, expanding the understanding of geometric analysis in such settings.

Contribution

It proposes novel curvature conditions that enable the derivation of key functional inequalities on manifolds with non-convex boundaries.

Findings

Established gradient estimates under new curvature conditions

Derived Harnack inequalities for manifolds with non-convex boundary

Proved transportation-cost inequalities in this geometric context

Abstract

In this article, new curvature conditions are introduced to establish functional inequalities including gradient estimates, Harnack inequalities and transportation-cost inequalities on manifolds with non-convex boundary.