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
Further geometry and topology for pseudo-holomorphic curves in complex Grassmannians Gm(CN) are studied. Some curvature pinching theorems for pseudo- holomorphic curyes with constant Kahler angles in Gm(CN) are obtain...Further geometry and topology for pseudo-holomorphic curves in complex Grassmannians Gm(CN) are studied. Some curvature pinching theorems for pseudo- holomorphic curyes with constant Kahler angles in Gm(CN) are obtained, so that the corresponding results for pseudoholomorphic curves in complex projective spaces are generalized.展开更多
基金Supported by the NSFC(11301273)Doctoral Discipline Foundation for Young Teachers in the Higher Education Institution of Ministry of Education(20123207120002)Natural Science Research of Jiangsu Higher Education Institutions of China(12KJD110004)
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.
文摘Further geometry and topology for pseudo-holomorphic curves in complex Grassmannians Gm(CN) are studied. Some curvature pinching theorems for pseudo- holomorphic curyes with constant Kahler angles in Gm(CN) are obtained, so that the corresponding results for pseudoholomorphic curves in complex projective spaces are generalized.
