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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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Cite

BibTeXRIS
BibTeX
@misc{wang2026hypersurfaces,
  title = {{Hypersurfaces of constant higher order mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity}},
  author = {Bin Wang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.01565},
  eprint = {2609.01565},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.01565},
}
RIS
TY  - UNPB
TI  - Hypersurfaces of constant higher order mean curvature in hyperbolic space with prescribed asymptotic boundary at infinity
AU  - Bin Wang
PY  - 2026
DA  - 2026/09/13
PB  - arXiv
DO  - 10.48550/arxiv.2609.01565
UR  - https://arxiv.org/abs/2609.01565
AB  - 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.
ER  -