Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivati...Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivatives of the second fundamental form. By use of a new maximumprinciple, some geometric properties at infinity are obtained.展开更多
An affirmative answer to a conjecture of K. Ogiue formulated in [2] is given, namely, thefollowing result is proved:Let Ma (n ≥ 2) be a complete Kaehler hypersurface immersed in a complex projective spaceCPn+1. Ifeve...An affirmative answer to a conjecture of K. Ogiue formulated in [2] is given, namely, thefollowing result is proved:Let Ma (n ≥ 2) be a complete Kaehler hypersurface immersed in a complex projective spaceCPn+1. Ifevery sectional curvature of Mn is positive, then Mn is totally geodesic in CPn+1.展开更多
基金Project supported by the National Natrual Science Foundation of China (No.10271106) the Natrual Science Foundation of Zhejiang Province, China (No.102033).
文摘Some geometric behaviours of complete solutions to mean curvature flow before the singu-larities occur are studied. The author obtains the estimates of the rate of the distance betweentwo fixed points and the derivatives of the second fundamental form. By use of a new maximumprinciple, some geometric properties at infinity are obtained.
文摘An affirmative answer to a conjecture of K. Ogiue formulated in [2] is given, namely, thefollowing result is proved:Let Ma (n ≥ 2) be a complete Kaehler hypersurface immersed in a complex projective spaceCPn+1. Ifevery sectional curvature of Mn is positive, then Mn is totally geodesic in CPn+1.
