What type of study is this?

This is a Quantitative Study study.

October 3, 2025Open Access

Curvature estimates for hypersurfaces of constant curvature in hyperbolic space II

Key Points

Estimates show that smooth complete hypersurfaces can exist under certain conditions in hyperbolic space.
The analysis extends earlier results, proving existence for all values of curvature rather than a restricted range.
This investigation derives curvature estimates to establish existence, differing from prior constrained approaches.
Broader implications could enhance understanding of geometric properties within hyperbolic space across various applications.

Abstract

In this note, we investigate the existence of smooth complete hypersurfaces in hyperbolic space with constant curvature and a prescribed asymptotic boundary at infinity. By deriving curvature estimates, we are able to deduce the existence in some cases. Previously, these existence results were proved for a restricted range of curvature values, while here we prove the existence for all possible curvature values.

Read Full Paperexternally

Bookmark

View Full Paper

Cite This Study

Bin Wang (Thu,) studied this question.

synapsesocial.com/papers/68e03501f0e39f13e7fa37ed https://doi.org/https://doi.org/10.48550/arxiv.2505.00760

Bookmark

View Full Paper