Entire self-expanders for power of σ curvature flow in Minkowski space
Entire self-expanders for power of σ curvature flow in Minkowski space
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DOI：
10.1016/j.jfa.2023.109866
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发表时间：
2023-01
影响因子：
1.7
通讯作者：
Zhizhang Wang;Ling Xiao
中科院分区：
文献类型：
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作者：
Zhizhang Wang;Ling Xiao
在文[19]中，我们证明了：如果一个完整的类空凸超曲面Mu0有有界主曲率，则从Mu0开始的σk 1/α(σk的幂)曲率流存在t>；0的光滑凸解u。此外，在重新标度后，流收敛到一个凸自扩张子M˜={(x，u˜(X))|x∈Rn}，它满足σk(κ[M˜])=(−<；X0，ν0>；)α.遗憾的是，在Minkowski空间中，σk曲率流的幂的自扩张子的存在性还没有被研究过。在本文中，我们填补了这一空白。
Abstract In [19], we prove that if an entire, spacelike, convex hypersurface M u 0 has bounded principal curvatures, then the σ k 1/α (power of σ k) curvature flow starting from M u 0 admits a smooth convex solution u for t> 0. Moreover, after rescaling, the flow converges to a convex self-expander M˜={(x, u˜(x))| x∈ R n} that satisfies σ k (κ [M˜])=(−< X 0, ν 0>) α. Unfortunately, the existence of self-expander for power of σ k curvature flow in Minkowski space has not been studied before. In this paper, we fill the gap.