Inverse mean curvature evolution of entire graphs
Inverse mean curvature evolution of entire graphs
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DOI：
10.1007/s00526-021-02160-w
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发表时间：
2017-09
影响因子：
2.1
通讯作者：
P. Daskalopoulos;G. Huisken
中科院分区：
文献类型：
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作者：
P. Daskalopoulos;G. Huisken
研究了严格平均凸整图在逆平均曲率流下的演化。首先证明了具有无穷大超线性增长的星形整图的全局存在性。本文的主要结果是关于渐近锥整凸图的临界情形。在这种情况下，我们表明，存在一个时间，这取决于增长在无穷大的初始数据，使唯一的解决方案的流量存在的所有。此外，当解收敛到一个平面上时.我们的技术利用了完全非线性流的超快扩散特性，这一特性意味着我们的解决方案在空间无穷远处的渐近行为对最大存在时间起着至关重要的影响，因为这种行为快速地向内部传播。
We study the evolution of strictly mean-convex entire graphs overbyInverse Mean Curvature flow. First we establish theglobal existenceof starshaped entire graphs withsuperlinear growthat infinity. The main result in this work concerns the critical case ofasymptotically conicalentire convex graphs. In this case we show that there exists a time, which depends on the growth at infinity of the initial data, such that the unique solution of the flow exists for all. Moreover, asthe solution converges to a flat plane. Our techniques exploit theultra-fast diffusioncharacter of the fully-nonlinear flow, a property that implies that the asymptotic behavior at spatial infinity of our solution plays a crucial influence on the maximal time of existence, as such behavior propagatesinfinitely fasttowards the interior.