This paper deals with the gradient estimates of the Hamilton type for the positive solutions to the following nonlinear diffusion equation：on a complete noncompact Riemannian manifold with a Bakry-Emery Ricci curvatu...This paper deals with the gradient estimates of the Hamilton type for the positive solutions to the following nonlinear diffusion equation：on a complete noncompact Riemannian manifold with a Bakry-Emery Ricci curvature bounded below by -K （K 〉 0）, where φ is a C2 function, a（x） and b（x） are C1 functions with certain conditions.展开更多
In a previous paper(Jiang and Yang(2021)),we constructed complete manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type but dimensions greater than...In a previous paper(Jiang and Yang(2021)),we constructed complete manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type but dimensions greater than or equal to 6.The purpose of the present paper is to use a different technique to exhibit a family of complete I-dimensional(I≥5)Riemannian manifolds of positive Ricci curvature,quadratically asymptotically nonnegative sectional curvature,and certain infinite Betti numbers bj(2≤j≤I-2).展开更多
It is our great pleasure to present the proceedings of the first Chinese-German Workshop on Metric Riemannian Geometry, which took place at Shanghai Jiao Tong University from October 12-16, 2015.
基金supported by the National Natural Science Foundation of China(Nos.11171253,11471175)the Fujian Provincial National Natural Science Foundation of China(No.2012J01015)+1 种基金the Startup Foundation for Introducing Talent of Nuist(No.2014r030)the Pre-research Foundation of NSFC(No.2014x025)
文摘This paper deals with the gradient estimates of the Hamilton type for the positive solutions to the following nonlinear diffusion equation：on a complete noncompact Riemannian manifold with a Bakry-Emery Ricci curvature bounded below by -K （K 〉 0）, where φ is a C2 function, a（x） and b（x） are C1 functions with certain conditions.
基金supported by National Natural Science Foundation of China(Grant Nos.11571228 and 12071283)fund of Shanghai Normal University(Grant No.SK202002)。
文摘In a previous paper(Jiang and Yang(2021)),we constructed complete manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type but dimensions greater than or equal to 6.The purpose of the present paper is to use a different technique to exhibit a family of complete I-dimensional(I≥5)Riemannian manifolds of positive Ricci curvature,quadratically asymptotically nonnegative sectional curvature,and certain infinite Betti numbers bj(2≤j≤I-2).
文摘It is our great pleasure to present the proceedings of the first Chinese-German Workshop on Metric Riemannian Geometry, which took place at Shanghai Jiao Tong University from October 12-16, 2015.
