Entire self-expanders for power of σ_k curvature flow in Minkowski space

2022/05/13 by Zhizhang Wang, Ling Xiao, Wang, Zhizhang +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2205.06853

openalex publication_date 2022/05/13 · openalex created_date 2022/05/22 · openalex updated_date 2026/07/28

Abstract

In [19], we prove that if an entire, spacelike, convex hypersurface M_u0 has bounded principal curvatures, then the σ_k^1/α (power of σ_k) curvature flow starting from M_u0 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∈ℝⁿ\ that satisfies σ_k(κ[M])=(-)^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.

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