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 th...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.展开更多
Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the followi...Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].展开更多
文摘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.
基金supported by the Fundamental Research Fund for the Central Universities
文摘Let （M,g, e^-fdv） be a smooth metric measure space. In this paper, we con- sider two nonlinear weighted p-heat equations. Firstly, we derive a Li-Yau type gradient estimates for the positive solutions to the following nonlinear weighted p-heat equationand f is a smooth function on M under the assumptionthat the m-dimensional nonnegative Bakry-Emery Ricci curvature. Secondly, we show an entropy monotonicity formula with nonnegative m-dimensional Bakry-Emery Ricci curva- ture which is a generalization to the results of Kotschwar and Ni [9], Li [7].
