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

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.

40 pages. arXiv admin note: text overlap with arXiv:1605.02493

References in corpus (3)

• On the geometry of Riemannian manifolds with density
• Rigidity phenomena in manifolds with boundary under a lower weighted Ricci curvature bound
• Rigidity of manifolds with boundary under a lower Bakry-E'mery Ricci curvature bound

Cited by in corpus (1)

• Concentration of $1$-Lipschitz functions on manifolds with boundary with Dirichlet boundary condition