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Arithmeticity, superrigidity, and totally geodesic submanifolds of infinite-volume hyperbolic manifolds

  • Nicholas Miller
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Abstract

Given an infinite-volume convex cocompact hyperbolic manifold with Fuchsian ends and infinitely many maximal properly immersed totally geodesic submanifolds of dimension at least two intersecting its convex core, we show that it (infinitely) covers an arithmetic hyperbolic manifold. This answers the general version of a question of Oh. As a byproduct of our techniques, we also give a Ratner-type classification of SO0(m,1)-invariant Radon measures whose support intersects the frame bundle of the interior of the convex core.

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Cite

BibTeXRIS
BibTeX
@misc{miller2026arithmeticity,
  title = {{Arithmeticity, superrigidity, and totally geodesic submanifolds of infinite-volume hyperbolic manifolds}},
  author = {Nicholas Miller},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.23594},
  eprint = {2610.23594},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.23594},
}
RIS
TY  - UNPB
TI  - Arithmeticity, superrigidity, and totally geodesic submanifolds of infinite-volume hyperbolic manifolds
AU  - Nicholas Miller
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2610.23594
UR  - https://arxiv.org/abs/2610.23594
AB  - Given an infinite-volume convex cocompact hyperbolic manifold with Fuchsian ends and infinitely many maximal properly immersed totally geodesic submanifolds of dimension at least two intersecting its convex core, we show that it (infinitely) covers an arithmetic hyperbolic manifold. This answers the general version of a question of Oh. As a byproduct of our techniques, we also give a Ratner-type classification of SO_0(m,1)-invariant Radon measures whose support intersects the frame bundle of the interior of the convex core.
ER  -