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
This paper mainly considers the translating soliton of H k-flow for k】0.We give the asymptotic expression of the entire rotationally symmetric translating soliton,and obtain non-convex'Wing-like'solution as w...This paper mainly considers the translating soliton of H k-flow for k】0.We give the asymptotic expression of the entire rotationally symmetric translating soliton,and obtain non-convex'Wing-like'solution as well as two barrier solutions.Moreover,we show that the solution with polynomial growth keeps its growth rate when evolution.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.
基金supported by National Natural Science Foundation of China(Grant Nos.10771189 and 10831008)
文摘This paper mainly considers the translating soliton of H k-flow for k】0.We give the asymptotic expression of the entire rotationally symmetric translating soliton,and obtain non-convex'Wing-like'solution as well as two barrier solutions.Moreover,we show that the solution with polynomial growth keeps its growth rate when evolution.
