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A finite Livshits theorem and local length spectrum rigidity

  • Jonathan DeWitt
  • Spencer Durham
  • James Marshall Reber
  • Thomas Aloysius O'Hare
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Abstract

We show that for closed negatively curved Riemannian manifolds whose length spectrum is exponentially separated, the length spectrum is a local isometry invariant. In particular, this holds for a dense set of negatively curved metrics. The main tool used in the proof is a finitary version of the Livshits theorem with an exponential tail.

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Cite

BibTeXRIS
BibTeX
@misc{dewitt2026finite,
  title = {{A finite Livshits theorem and local length spectrum rigidity}},
  author = {Jonathan DeWitt and Spencer Durham and James Marshall Reber and Thomas Aloysius O'Hare},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.23762},
  eprint = {2609.23762},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.23762},
}
RIS
TY  - UNPB
TI  - A finite Livshits theorem and local length spectrum rigidity
AU  - Jonathan DeWitt
AU  - Spencer Durham
AU  - James Marshall Reber
AU  - Thomas Aloysius O'Hare
PY  - 2026
DA  - 2026/09/20
PB  - arXiv
DO  - 10.48550/arxiv.2609.23762
UR  - https://arxiv.org/abs/2609.23762
AB  - We show that for closed negatively curved Riemannian manifolds whose length spectrum is exponentially separated, the length spectrum is a local isometry invariant. In particular, this holds for a dense set of negatively curved metrics. The main tool used in the proof is a finitary version of the Livshits theorem with an exponential tail.
ER  -