Deforming two-dimensional graphs in R4 by forced mean curvature flow

Kodai Mathematical Journal

Jing Mao¹ 

[1] Departamento de Matemática Instituto Superior Técnico Technical University of Lisbon

关键词: Global solution;    Backward heat kernel;    Mean curvature flow;   

DOI  :  10.2996/kmj/1352985452

学科分类：数学（综合）

来源: Tokyo Institute of Technology, Department of Mathematics

【 摘 要 】

References(11)A surface Σ0 is a graph in R4 if there is a unit constant 2-form w in R4 such that ‹e1 ∧ e2, w› ≥ v0 > 0, where {e1, e2} is an orthonormal frame on Σ0. In this paper, we investigate a 2-dimensional surface Σ evolving along a mean curvature flow with a forcing term in direction of the position vector. If v0 ≥ ${1 \over \sqrt {2}}$ holds on the initial graph Σ0 which is the immersion of the surface Σ, and the coefficient function of the forcing vector is nonnegative, then the forced mean curvature flow has a global solution, which generalizes part of the results of Chen-Li-Tian in [2].

【 授权许可】

Unknown