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首页> 外文期刊>Kodai Mathematical Journal >Deforming two-dimensional graphs in R4 by forced mean curvature flow
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Deforming two-dimensional graphs in R4 by forced mean curvature flow

机译:通过强制平均曲率流使R4中的二维图变形

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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].
机译:参考文献(11)如果R4中存在单位常数2形式w,使得‹e1∧e2,w›≥v0> 0,其中{e1,e2}是Σ0上的正交框架,则曲面Σ0是R4中的图。在本文中,我们研究了沿着平均曲率流演化的二维表面Σ,该二维曲面在位置矢量的方向上带有强迫项。如果v0≥$ {1 over sqrt {2}} $保留在初始图Σ0上,该初始图是表面Σ的浸入,且力矢量的系数函数为非负值,则强制平均曲率流具有全局解决方案,它概括了[2]中陈立田的部分结果。

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