Manifolds with Bakry-Emery Ricci Curvature Bounded Below

Abstract

In this paper we show that, under some conditions, if M is a manifold with Bakry-Émery Ricci curvature bounded below and with bounded potential function then M is compact. We also establish a volume comparison theorem for manifolds with nonnegative Bakry-Émery Ricci curvature which allows us to prove a topolological rigidity theorem for such manifolds.

Some Myers-Type Theorems and Comparison Theorems for Manifolds with Modified Ricci Curvature

“…In [3] the first and the third authors of this paper proved the following theorem: Theorem 1.4. Let (M, g, e −f dvol g ) be a metric espace such that Ric f ≥ −(n − 1)k 2 .…”