Curvature estimates for semi-convex solutions of asymptotic Plateau problem in ℍⁿ⁺¹

2024/08/18 by Hong Han, Hong, Han, Ruijia Zhang +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.2408.09428

Abstract

In this paper, we consider the asymptotic σ_k Plateau problem in hyperbolic space. We establish C² estimates for semi-convex complete hypersurfaces satisfying constant σ_k curvature with a prescribed asymptotic boundary at the infinity for 2≤ k≤ n-2 . The result is based on a new crucial concavity inequality derived for hessian equations.

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• Hypersurfaces of constant sum Hessian curvature in Hyperbolic space

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