This paper mainly deals with the type II singularities of the mean curvature flow from a symplectic surface or from an almost calibrated Lagrangian surface in a K¨ahler surface.The relation between the maximum of...This paper mainly deals with the type II singularities of the mean curvature flow from a symplectic surface or from an almost calibrated Lagrangian surface in a K¨ahler surface.The relation between the maximum of the Kahler angle and the maximum of |H|2 on the limit flow is studied.The authors also show the nonexistence of type II blow-up flow of a symplectic mean curvature flow which is normal flat or of an almost calibrated Lagrangian mean curvature flow which is flat.展开更多
In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive pa...In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive part u+(z)=max{u(z),0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.展开更多
基金Project supported by the National Natural Science Foundation of China (Nos. 10901088, 11001268)
文摘This paper mainly deals with the type II singularities of the mean curvature flow from a symplectic surface or from an almost calibrated Lagrangian surface in a K¨ahler surface.The relation between the maximum of the Kahler angle and the maximum of |H|2 on the limit flow is studied.The authors also show the nonexistence of type II blow-up flow of a symplectic mean curvature flow which is normal flat or of an almost calibrated Lagrangian mean curvature flow which is flat.
基金the National Natural Science Foundation of China(No.10671022)Research Foundation for Doctor Programme (No.20060027023)Henan Institute of Education Youth Scientific Research Fund (No.20070107)
文摘In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive part u+(z)=max{u(z),0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.
