The $$Q_k$$ flow on complete non-compact graphs
The $$Q_k$$ flow on complete non-compact graphs
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DOI：
10.1007/s00526-021-02162-8
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发表时间：
2016-03
影响因子：
2.1
通讯作者：
K. Choi;P. Daskalopoulos
中科院分区：
文献类型：
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作者：
K. Choi;P. Daskalopoulos
我们建立了由流旋转的完全非紧弱凸光滑超曲面的长期存在性。我们证明最大存在时间T取决于向量空间W:={w∈Rn+1:supX∈Σ0|⟨X,w⟩|=+∞}的维度，其中包含初始数据无限的每个方向。如果，则解永远存在；如果，那么解在某个有限时间内存在。在后一种情况下，解的无穷远处迹是维流的闭凸粘度解。
We establish the long time existence of complete non-compact weakly convex and smooth hypersurfacesevolving by the-flow. We show that the maximum existence timeTdepends on the dimensionof the vector space W:={w∈Rn+1:supX∈Σ0|⟨X,w⟩|=+∞} which contains each direction in which our initial datais infinite. If, then the solutionexists for all time; if, then the solutionexsist up to some finite time. In the latter case, thetrace at infinityof the solutionis a closed convex viscosity solution of the-dimensionalflow on.