The asymptotic Plateau problem for Hypersurfaces of constant $H_{k}$ curvature in hyperbolic space
Year: 2026
Type: preprint
Abstract: In this paper, we study the asymptotic Plateau problem in hyperbolic space for hypersurfaces of constant $H_k$-curvature. We prove the existence of a smooth complete $k$-convex hypersurface in $\mathbb{H}^{n+1}$ satisfying \[ H_k(κ)=σ, \qquad σ\in(0,1), \] with prescribed asymptotic boundary at infinity. In particular, our result extends the range of the constant $σ$ in the existence theorem of Guan and Spruck [J. Eur. Math. Soc. 12 (2010), no. 3, 797--817] for $H_{k}$ curvature to the full interval $(0,1)$.
Source: arXiv (Cornell University)
Authors: Mei, Xinqun, Yan, Jin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7206163258