PreprintarXiv licencearXiv
The asymptotic Plateau problem for Hypersurfaces of constant Hk curvature in hyperbolic space
Abstract
In this paper, we study the asymptotic Plateau problem in hyperbolic space for hypersurfaces of constant Hk-curvature. We prove the existence of a smooth complete k-convex hypersurface in ℍn+1 satisfying Hk(κ)=σ, σ∈(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 Hk curvature to the full interval (0,1).
Related
- Hypersurfaces of constant higher order mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity
- The Asymptotic Plateau Problem for p-Convex Hypersurfaces in Hyperbolic Space
- Hypersurfaces with constant sectional curvature of a product of two space forms
- Stable Constant Mean Curvature Hypersurfaces in ℍn
- On the structure of stable constant anisotropic mean curvature hypersurfaces
BibTeX
@misc{mei2026asymptotic,
title = {{The asymptotic Plateau problem for Hypersurfaces of constant $H_k$ curvature in hyperbolic space}},
author = {Xinqun Mei and Jin Yan},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.01104},
eprint = {2609.01104},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.01104},
}
RIS
TY - UNPB
TI - The asymptotic Plateau problem for Hypersurfaces of constant H_k curvature in hyperbolic space
AU - Xinqun Mei
AU - Jin Yan
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.01104
UR - https://arxiv.org/abs/2609.01104
AB - 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 ℍ^n+1 satisfying H_k(κ)=σ, σ∈(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).
ER -