Motion Of Level Set By General Curvature
Motion Of Level Set By General Curvature
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发表时间：
2016-02
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通讯作者：
Ling Xiao
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作者：
Ling Xiao
在本文中，我们通过一般曲率研究水平集的运动。这种设置的困难在于，一般曲率函数只能在允许的圆锥体中明确定义。为了将一般曲率流的弱解的存在性扩展到锥体之外，我们引入了一个新的近似函数$\hat{f}^n$（参见（3.1））。此外，利用[4]中的思想，我们给出了完全非线性曲率流中Ben-Andrews非塌缩结果的椭圆方法；我们希望这种方法可以推广到更广泛的椭圆方程。
In this paper, we study the motion of level sets by general curvature. The difficulty of this setting is that a general curvature function is only well defined in an admissible cone. In order to extend the existence of a weak solution of a general curvature flow to outside the cone we introduce a new approximation function $\hat{f}^n$ (see (3.1)). Moreover, using the idea in [4], we give an elliptic approach for the Ben-Andrews' non-collapsing result in fully nonlinear curvature flows; we hope this approach can be generalized to a wider class of elliptic equations.