Comparison theorems on smooth metric measure spaces with boundary-Reference-Cited by-同舟云学术

Comparison theorems on smooth metric measure spaces with boundary

Published:2016-10-01 Issue:4 Volume:16 Page:401-411
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Feng Wang Lin¹,Zhang Ze Yu¹,Zhou Yu Jie¹

Affiliation:

1. School of Science, Nantong University, Nantong 226007, China

Abstract

Abstract In this paper we study smooth metric measure spaces with boundary via the Bakry–Émery curvature and the weighted mean curvature of the boundary. We establish the weighted Laplacian comparison theorems and the upper bound estimates of the distance from any point of the manifold to its boundary. As applications, we derive lower bound estimates for the first Dirichlet eigenvalue.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2016-0022/pdf

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