On Gage-Hamilton's entropy formula and Harnack inequality for the curve shortening flow
On Gage-Hamilton's entropy formula and Harnack inequality for the curve shortening flow
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DOI：
10.1016/j.difgeo.2022.101959
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发表时间：
2023-02
影响因子：
0.5
通讯作者：
Hongxin Guo;Shengmao Zhu
中科院分区：
文献类型：
--
作者：
Hongxin Guo;Shengmao Zhu
利用Gage和汉密尔顿首先对平面上曲线缩短流研究的曲率Boltzmann熵的前两阶导数，定义了一个单调性公式，该公式除在收缩圆上外是严格递增的.通过逐点计算给出了Gage-Hamilton Harnack不等式的另一种证明。
By the first two derivatives of the Boltzmann entropy of the curvature, which was first studied by Gage and Hamilton for the curve shortening flow in the plane, we define a monotonicity formula which is strictly increasing unless on a shrinking circle. By calculating pointwisely we give an alternate proof of Gage-Hamilton's Harnack inequality.