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arXiv · 2609.01565

Hypersurfaces of constant higher order mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity

Bin Wang
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Abstract

In this note, we prove the existence of smooth complete admissible hypersurfaces in hyperbolic space with constant higher order mean curvature and a prescribed asymptotic boundary at infinity. The result holds for a large part of indices in the subcritical range where the concavity inequality loses its effectiveness. We supply with new arguments to reduce the proof to a semi-convex situation in which case the concavity inequality can play a role.

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Bin Wang. 2026-09-13. Hypersurfaces of constant higher order mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity. https://arxiv.org/abs/2609.01565

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