Sobolev Inequality on Manifolds With Asymptotically Nonnegative Bakry-\'Emery Ricci Curvature

TL;DR

This paper establishes a Sobolev inequality for manifolds with density that have asymptotically nonnegative Bakry-Émery Ricci curvature, extending geometric analysis tools to broader classes of manifolds.

Contribution

It introduces a Sobolev inequality applicable to manifolds with density and specific curvature conditions, broadening the scope of geometric inequalities.

Findings

Proves a Sobolev inequality under asymptotically nonnegative Bakry-Émery Ricci curvature.

Extends previous results to manifolds with density and curvature decay conditions.

Provides tools for analysis on non-compact manifolds with weighted measures.

Abstract

In this paper, inspired by [4, 9], we prove a Sobolev inequality on manifolds with density and asymptotically nonnegative Bakry-\'Emery Ricci curvature.