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
In this paper, we study the integrals of the Ricci curvature over metric balls in a Finsler manifold,which can be viewed as an L^(q)-norm of the Ricci curvature. By bounding such integrals from above, we obtain severa...In this paper, we study the integrals of the Ricci curvature over metric balls in a Finsler manifold,which can be viewed as an L^(q)-norm of the Ricci curvature. By bounding such integrals from above, we obtain several Myers type theorems.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 National Natural Science Foundation of China(Grant Nos.11501202 and 11761058)the grant of China Scholarship Council。
文摘In this paper, we study the integrals of the Ricci curvature over metric balls in a Finsler manifold,which can be viewed as an L^(q)-norm of the Ricci curvature. By bounding such integrals from above, we obtain several Myers type theorems.
