闵科夫斯基空间中的平移解和全黑森曲率流

arXiv - MATH - Analysis of PDEs Pub Date : 2024-09-11 DOI:arxiv-2409.07301

Qu Changzheng, Wang Zhizhang, Wo Weifeng

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摘要

本文研究闵科夫斯基空间中非紧凑空间似超曲面的 $k$-Hessian 曲率流。我们首先证明了具有给定渐近行为的平移解的存在性。然后，我们证明对于满足特定条件的严格凸初始超曲面，曲率流在所有时间内都存在，并且归一化流收敛于平移解。

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Translating solutions and the entire Hessian curvature flow in Minkowski space

In this paper, we study the $k$-Hessian curvature flow of noncompact spacelike hypersurfaces in Minkowski space. We first prove the existence of translating solutions with given asymptotic behavior. Then, we prove that for strictly convex initial hypersurface satisfying certain conditions, the curvature flow exists for all time, and the normalized flow converges to a translating solution.

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arXiv - MATH - Analysis of PDEs

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