Comparison geometry of manifolds with boundary under a lower weighted Ricci curvature bound

TL;DR

This paper investigates Riemannian manifolds with boundary under a lower weighted Ricci curvature bound, deriving comparison geometric results based on curvature and boundary conditions.

Contribution

It introduces new comparison theorems for manifolds with boundary under a lower weighted Ricci curvature bound involving the density function.

Findings

Derived comparison geometric results under the curvature condition

Established bounds for weighted mean curvature of the boundary

Extended classical comparison theorems to weighted Ricci curvature setting

Abstract

We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition, and a suitable condition for the weighted mean curvature for the boundary, we obtain various comparison geometric results.