In this article, we concern on complete manifolds with finite volume. We prove that under some assumptions about scalar curvature and the Yamabe constant, the manifolds must be compact, and we also give the diameter e...In this article, we concern on complete manifolds with finite volume. We prove that under some assumptions about scalar curvature and the Yamabe constant, the manifolds must be compact, and we also give the diameter estimates in terms of the scalar curvature and the Yamabe constant.展开更多
The global existence of the heat flow for harmonic maps from noncompact manifolds is considered. When L^m norm of the gradient of initial data is small, the existence of a global solution is proved.
The author considers harmonic maps on complete noncompact manifolds, solves the Dirichlet problem in manifolds with nonnegative sectional curvature out of a compact set, and proves the Fatou theorem for harmonic maps ...The author considers harmonic maps on complete noncompact manifolds, solves the Dirichlet problem in manifolds with nonnegative sectional curvature out of a compact set, and proves the Fatou theorem for harmonic maps into convex balls.展开更多
In this paper,the author solves the Dirichlet problem for Hermitian-Poisson metric equation√(-1)Λ_(ω)G_(H)=λId and proves the existence of Hermitian-Poisson metrics on flat bundles over a class of complete Hermiti...In this paper,the author solves the Dirichlet problem for Hermitian-Poisson metric equation√(-1)Λ_(ω)G_(H)=λId and proves the existence of Hermitian-Poisson metrics on flat bundles over a class of complete Hermitian manifolds.Whenλ=0,the HermitianPoisson metric is a Hermitian harmonic metric.展开更多
In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we ...In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we obtain the Aronson′s estimate for the operator 1/2△+b,which can be regarded as an extension of Peter Li and S.T.Yau's heat kernel estimate for the Laplace-Beltrami operator.展开更多
Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(...Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(‖▽f‖p+‖fp) (2≤p＜q＜∞) is given.展开更多
We use analytic methods in this paper to prove some new Enoki type injeetivity theorems on compact complex manifolds which generalize more or less the original Enoki injectivity theorem.
文摘In this article, we concern on complete manifolds with finite volume. We prove that under some assumptions about scalar curvature and the Yamabe constant, the manifolds must be compact, and we also give the diameter estimates in terms of the scalar curvature and the Yamabe constant.
基金Supported by the National Natural Science Foundation of China (1057115610671079+1 种基金10701064)the Zijin Project of Zhejiang University
文摘The global existence of the heat flow for harmonic maps from noncompact manifolds is considered. When L^m norm of the gradient of initial data is small, the existence of a global solution is proved.
文摘The author considers harmonic maps on complete noncompact manifolds, solves the Dirichlet problem in manifolds with nonnegative sectional curvature out of a compact set, and proves the Fatou theorem for harmonic maps into convex balls.
文摘In this paper,the author solves the Dirichlet problem for Hermitian-Poisson metric equation√(-1)Λ_(ω)G_(H)=λId and proves the existence of Hermitian-Poisson metrics on flat bundles over a class of complete Hermitian manifolds.Whenλ=0,the HermitianPoisson metric is a Hermitian harmonic metric.
文摘In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we obtain the Aronson′s estimate for the operator 1/2△+b,which can be regarded as an extension of Peter Li and S.T.Yau's heat kernel estimate for the Laplace-Beltrami operator.
基金Project supported by the National Natural Science Foundation of China (No.10271107) the 973 Project of the Ministry of Science and Technology of China (No.G1999075105) the Zhejiang Provincial Natural Science Foundation of China (No.RC97017).
文摘Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(‖▽f‖p+‖fp) (2≤p＜q＜∞) is given.
文摘We use analytic methods in this paper to prove some new Enoki type injeetivity theorems on compact complex manifolds which generalize more or less the original Enoki injectivity theorem.
