Rigidity of complete manifolds with weighted Poincaré inequality (2208.05077v2)

Published 9 Aug 2022 in math.DG and math.AP

Abstract: We consider complete Riemannian manifolds which satisfy a weighted Poincar`e inequality and have the Ricci curvature bounded below in terms of the weight function. When the weight function has a non-zero limit at infinity, the structure of this class of manifolds at infinity are studied and certain splitting result is obtained. Our result can be viewed as an improvement of Li-Wang's result in \cite{LW3}.

Summary

We haven't generated a summary for this paper yet.

Whiteboard

Generate a whiteboard explanation of this paper.

Sign Up to Generate

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

Top Community Prompts

Explain it Like I'm 14

Practical Applications

Conceptual Simplification

Sign Up to Activate View All Prompts

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Continue Learning

We haven't generated follow-up questions for this paper yet.

Authors (1)

Lihan Wang

Collections

Sign up for free to add this paper to one or more collections.