In this paper, we derive a series of gradient estimates and Harnack inequalities for positive solutions of a Yamabe-type parabolic partial differential equation (△-■t)u=pu+qu^(a+1) under the Yamabe flow. Here p,q∈C...In this paper, we derive a series of gradient estimates and Harnack inequalities for positive solutions of a Yamabe-type parabolic partial differential equation (△-■t)u=pu+qu^(a+1) under the Yamabe flow. Here p,q∈C^(2,1)(M^(n)×[0,T]) and a is a positive constant.展开更多
In this paper,we study the CR(Cauchy-Riemann)Yamabe flow with zero CR Yamabe invariant.We use the CR Poincaréinequality and a Gagliardo-Nirenberg type interpolation inequality to show that this flow has the long ...In this paper,we study the CR(Cauchy-Riemann)Yamabe flow with zero CR Yamabe invariant.We use the CR Poincaréinequality and a Gagliardo-Nirenberg type interpolation inequality to show that this flow has the long time solution and the solution converges to a contact form with flat pseudo-Hermitian scalar curvature exponentially.展开更多
In this paper,we study the discrete Morse flow for either Yamabe type heat flow or nonlinear heat flow on a bounded regular domain in the whole space.We show that under suitable assumptions on the initial data g one h...In this paper,we study the discrete Morse flow for either Yamabe type heat flow or nonlinear heat flow on a bounded regular domain in the whole space.We show that under suitable assumptions on the initial data g one has a weak approxi-mate discrete Morse flow for the Yamabe type heat flow on any time interval.This phenomenon is very different from the smooth Yamabe flow,where the finite time blow up may exist.展开更多
In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain family of geometric operators under some geometric flows.In an attempt to understand the arising simila...In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain family of geometric operators under some geometric flows.In an attempt to understand the arising similarities we formulate two conjectures on the monotonicity of the eigenvalues of Schrodinger operators under geometric flows.We also pose three questions which we consider to be of a general interest.展开更多
文摘In this paper, we derive a series of gradient estimates and Harnack inequalities for positive solutions of a Yamabe-type parabolic partial differential equation (△-■t)u=pu+qu^(a+1) under the Yamabe flow. Here p,q∈C^(2,1)(M^(n)×[0,T]) and a is a positive constant.
基金supported by National Natural Science Foundation of China(Grant No.11571304)。
文摘In this paper,we study the CR(Cauchy-Riemann)Yamabe flow with zero CR Yamabe invariant.We use the CR Poincaréinequality and a Gagliardo-Nirenberg type interpolation inequality to show that this flow has the long time solution and the solution converges to a contact form with flat pseudo-Hermitian scalar curvature exponentially.
基金supported in part by Young Faculty Career Start Program (34000-3171917)NSFC (10901165)+1 种基金NSFGD (9451027501002600)China Postdoc-toral Science Foundation (20090460066)
文摘In this article, the author proves a compactness result about Riemannian manifolds with an arbitrary pointwisely pinched Ricci curvature tensor.
文摘In this paper,we study the discrete Morse flow for either Yamabe type heat flow or nonlinear heat flow on a bounded regular domain in the whole space.We show that under suitable assumptions on the initial data g one has a weak approxi-mate discrete Morse flow for the Yamabe type heat flow on any time interval.This phenomenon is very different from the smooth Yamabe flow,where the finite time blow up may exist.
文摘In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain family of geometric operators under some geometric flows.In an attempt to understand the arising similarities we formulate two conjectures on the monotonicity of the eigenvalues of Schrodinger operators under geometric flows.We also pose three questions which we consider to be of a general interest.
