Spectral theory of frame flows on closed hyperbolic manifolds

Julien Namazi

Spectral theory of frame flows on closed hyperbolic manifolds

Dynamical Systems 2026-07-31 v1 Analysis of PDEs Differential Geometry

Authors: Julien Namazi

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 an extensive use of the Borel-Weil calculus developed in [https://arxiv.org/abs/2405.14846] to overcome difficulties of this higher-dimensional case.

Keywords

frame flows hyperbolic manifolds resolvent estimates spectral gap exponential mixing Borel-Weil calculus

Cite

@article{arxiv.2607.29319,
  title  = {Spectral theory of frame flows on closed hyperbolic manifolds},
  author = {Julien Namazi},
  journal= {arXiv preprint arXiv:2607.29319},
  year   = {2026}
}

Comments

56 pages, 1 figure