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PreprintCC BY-NC-SA 4.0arXiv

Spectral theory of frame flows on closed hyperbolic manifolds

  • Julien Namazi
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Abstract

We prove a resolvent estimate for the generator of the frame flow on hyperbolic manifolds away from vertical lines of resonances. A byproduct of the proof is an optimal essential spectral gap property for the generator, hence giving another proof of exponential mixing of frame flows with respect to the volume measure of the frame bundle. This extends the result of [https://arxiv.org/abs/2005.08387v2] in dimension 3 to any dimension. We make extensive use of the Borel-Weil calculus developed in [https://arxiv.org/abs/2405.14846] to overcome difficulties of this higher-dimensional case.

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Cite

BibTeXRIS
BibTeX
@misc{namazi2026spectral,
  title = {{Spectral theory of frame flows on closed hyperbolic manifolds}},
  author = {Julien Namazi},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2607.29319},
  eprint = {2607.29319},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.29319},
  note = {CC BY-NC-SA 4.0},
}
RIS
TY  - UNPB
TI  - Spectral theory of frame flows on closed hyperbolic manifolds
AU  - Julien Namazi
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2607.29319
UR  - https://arxiv.org/abs/2607.29319
AB  - We prove a resolvent estimate for the generator of the frame flow on hyperbolic manifolds away from vertical lines of resonances. A byproduct of the proof is an optimal essential spectral gap property for the generator, hence giving another proof of exponential mixing of frame flows with respect to the volume measure of the frame bundle. This extends the result of [https://arxiv.org/abs/2005.08387v2] in dimension 3 to any dimension. We make extensive use of the Borel-Weil calculus developed in [https://arxiv.org/abs/2405.14846] to overcome difficulties of this higher-dimensional case.
ER  -