Gradient flow for the Willmore functional
Gradient flow for the Willmore functional
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DOI：
10.4310/cag.2002.v10.n2.a4
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发表时间：
2002
影响因子：
0.7
通讯作者：
E. Kuwert;R. Schätzle
中科院分区：
文献类型：
--
作者：
E. Kuwert;R. Schätzle
我们考虑二维的，紧凑的浸入表面在R移动的梯度的L积分的曲率。目前还不知道这个四阶几何演化方程的解是否会在有限时间内产生奇点。我们给出了一个光滑解的寿命的下界，它只取决于初始曲面的曲率在空间中集中的程度。
We consider two-dimensional, compact immersed surfaces in R moving by the gradient of the L integral of their curvature. It is not known whether solutions to this fourth-order, geometric evolution equation may develop singularities in finite time. We give a lower bound on the lifespan of a smooth solution, which depends only on how much the curvature of the initial surface is concentrated in space.