In this paper, we study the complex structure and curvature decay of Kahler manifolds with nonnegative curvature. Using a recent result obtained by Ni-Shi-Tam, we get a gap theorem of Ricci curvature on Kahler manifold.
In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality...In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.展开更多
We give a survey of results on the construction of and obstructions to metrics of almost nonnegative curvature operator on closed manifolds and results on the cohomology rings of closed, simply-connected manifolds wit...We give a survey of results on the construction of and obstructions to metrics of almost nonnegative curvature operator on closed manifolds and results on the cohomology rings of closed, simply-connected manifolds with a lower curvature and upper diameter bound. The latter is motivated by a question of Grove whether these condition imply finiteness of rational homotopy types. This question has answers by F. Fang-X. Rong, B. Totaro and recently A. Dessai and the present author.展开更多
The authors prove the space of harmonic functions with polynomial growth of a fixed rate on a complete noncompact Riemannian manifold with asymptotically nonnegative curvature is finite dimensional.
The present paper is concerned with the existence of golbal smooth solutions for the homogeneous Dirichlet boundary value problem of the Darboux equation and the case degenerate onthe boundary is contained As some app...The present paper is concerned with the existence of golbal smooth solutions for the homogeneous Dirichlet boundary value problem of the Darboux equation and the case degenerate onthe boundary is contained As some applications the smooth isometric embeddings of positivelyand nonnegatively curved disks into R^3 are constructed.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
In this paper, we prove that if M is an open manifold with nonnegativeRicci curvature and large volume growth, positive critical radius, then sup Cp = ∞.As an application, we give a theorem which supports strongly Pe...In this paper, we prove that if M is an open manifold with nonnegativeRicci curvature and large volume growth, positive critical radius, then sup Cp = ∞.As an application, we give a theorem which supports strongly Petersen's conjecture.展开更多
in this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature, large volume growth has finite topological type provided that lim r→∞{（vol[B（p.r]/ωnrn-αM）rk（n-1...in this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature, large volume growth has finite topological type provided that lim r→∞{（vol[B（p.r]/ωnrn-αM）rk（n-1）/k＋1（1-α/2）}≤for some COllstant ε〉0 We also prove that a conlplete Riemannian manifold with nonnegative kth-Ricci curvature and undler some pinching conditions is diffeomorphic to R^n.展开更多
In this paper, we study complete open manifolds with nonnegative Ricci curvature and injectivity radius bounded from below. We find that this kind of manifolds are diffeomorphic to a Euclidean space when certain dista...In this paper, we study complete open manifolds with nonnegative Ricci curvature and injectivity radius bounded from below. We find that this kind of manifolds are diffeomorphic to a Euclidean space when certain distance functions satisfy a reasonable condition.展开更多
The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension.Like t...The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension.Like the Michael-Simon Sobolev inequality,this inequality includes a term involving the mean curvature.This extends a recent result of Brendle with Euclidean setting.展开更多
基金Foundation item： Supported by the Natural Science Foundation of Zhejiang Province（LY13A010018）
文摘In this paper, we study the complex structure and curvature decay of Kahler manifolds with nonnegative curvature. Using a recent result obtained by Ni-Shi-Tam, we get a gap theorem of Ricci curvature on Kahler manifold.
基金Supported by the NSFC(11771087,12171091 and 11831005)。
文摘In this note,we prove a logarithmic Sobolev inequality which holds for compact submanifolds without a boundary in manifolds with asymptotically nonnegative sectional curvature.Like the Michale-Simon Sobolev inequality,this inequality contains a term involving the mean curvature.
文摘We give a survey of results on the construction of and obstructions to metrics of almost nonnegative curvature operator on closed manifolds and results on the cohomology rings of closed, simply-connected manifolds with a lower curvature and upper diameter bound. The latter is motivated by a question of Grove whether these condition imply finiteness of rational homotopy types. This question has answers by F. Fang-X. Rong, B. Totaro and recently A. Dessai and the present author.
基金Project supported by the National Natural Science Foundation of China (No.10271089).
文摘The authors prove the space of harmonic functions with polynomial growth of a fixed rate on a complete noncompact Riemannian manifold with asymptotically nonnegative curvature is finite dimensional.
文摘The present paper is concerned with the existence of golbal smooth solutions for the homogeneous Dirichlet boundary value problem of the Darboux equation and the case degenerate onthe boundary is contained As some applications the smooth isometric embeddings of positivelyand nonnegatively curved disks into R^3 are constructed.
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In this paper, we prove that if M is an open manifold with nonnegativeRicci curvature and large volume growth, positive critical radius, then sup Cp = ∞.As an application, we give a theorem which supports strongly Petersen's conjecture.
文摘in this paper,we prove that a complete n-dimensional Riemannian manifold with nonnegative kth-Ricci curvature, large volume growth has finite topological type provided that lim r→∞{（vol[B（p.r]/ωnrn-αM）rk（n-1）/k＋1（1-α/2）}≤for some COllstant ε〉0 We also prove that a conlplete Riemannian manifold with nonnegative kth-Ricci curvature and undler some pinching conditions is diffeomorphic to R^n.
文摘In this paper, we study complete open manifolds with nonnegative Ricci curvature and injectivity radius bounded from below. We find that this kind of manifolds are diffeomorphic to a Euclidean space when certain distance functions satisfy a reasonable condition.
基金supported by the National Natural Science Foundation of China(No.12271163)the Science and Technology Commission of Shanghai Municipality(No.22DZ2229014)Shanghai Key Laboratory of PMMP.
文摘The authors prove a sharp logarithmic Sobolev inequality which holds for compact submanifolds without boundary in Riemannian manifolds with nonnegative sectional curvature of arbitrary dimension and codimension.Like the Michael-Simon Sobolev inequality,this inequality includes a term involving the mean curvature.This extends a recent result of Brendle with Euclidean setting.
