Lipschitz Continuous Hypersurfaces with Prescribed Curvature and Asymptotic Boundary in Hyperbolic Space

2020/10/07 by Zhenan Sui, Wei Sun, Sui, Zhenan +1 · 1 citation
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2010.03479

Abstract

We prove the existence of a complete locally Lipschitz continuous hypersurface in weak sense with prescribed Weingarten curvature and asymptotic boundary at infinity in hyperbolic space under certain assumptions.

Citations

• Interior curvature bounds for a class of curvature equations

Cited by

• Embedded convex surfaces in hyperbolic and anti-de Sitter spaces

Related

• Hypersurfaces of Constant Curvature in Hyperbolic Space I
• Curvature estimates for hypersurfaces of constant curvature in hyperbolic space II
• Convex Hypersurfaces with Prescribed Scalar Curvature and Asymptotic Boundary in Hyperbolic Space
• Hypersurfaces of Constant Curvature in Hyperbolic Space II
• Smooth Solutions to Asymptotic Plateau Type Problem in Hyperbolic Space