Dual flows in hyperbolic space and de Sitter space

2016/04/08 by Hao Yu, Yu, Hao · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1604.02369

openalex publication_date 2016/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider contracting flows in (n+1)-dimensional hyperbolic space and expanding flows in (n+1)-dimensional de Sitter space. When the flow hypersurfaces are strictly convex we relate the contracting hypersurfaces and the expanding hypersurfaces by the Gauss map. The contracting hypersurfaces shrink to a point x₀ in finite time while the expanding hypersurfaces converge to the maximal slice \ τ=0\. After rescaling, by the same scale factor, the resclaed contracting hypersurfaces converge to a unit geodesic sphere, while the rescaled expanding hypersufaces converge to slice \ τ= -1\ exponential fast in C^∞(\mathbbSⁿ).

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