Skip to content
DraconiticResearch
Search Sources API
186,541 studies31 sourcesUpdated 48 min ago
PreprintCC BY 4.0arXiv

Local unmarked length spectrum rigidity for hyperbolic surfaces

  • Tristan Humbert
Open at sourcePDFDOICite

Abstract

Let (M,g) be a closed negatively curved surface. If g is strictly 1/9-pinched and has the same unmarked length spectrum as a hyperbolic metric, we show that g is hyperbolic. As a consequence, we show that any hyperbolic metric on a surface admits a C2-neighborhood in the space of metrics in which it is characterized by its unmarked length spectrum, up to isometry.

Related

  1. Length spectrum rigidity and flexibility of spheres of revolution with one equator
    Alberto Abbondandolo, Marco Mazzucchelli
    HALPreprintPublisher termsFull textGeneral mathematicsHAL
  2. Length bounds and rigidity for ancient curve shortening flow on warped product surfaces
    Beomseok Goh, Taehun Lee
    arXivPreprintarXiv licenceFull textAnalysis & PDEsGeometry & topologyarXiv
  3. A finite Livshits theorem and local length spectrum rigidity
    Jonathan DeWitt, Spencer Durham, James Marshall Reber +1
    arXivPreprintarXiv licenceFull textDynamical systemsGeometry & topologyarXiv
  4. Verified Length Spectrum and Margulis number for Hyperbolic 3-Manifolds
    Matthias Goerner, Robert C. Haraway III, Neil R. Hoffman +1
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. Rigidity Theorems for the Weyl Problem of Convex Surfaces in Hyperbolic 3-Space
    Xinrong Zhao
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{humbert2026local,
  title = {{Local unmarked length spectrum rigidity for hyperbolic surfaces}},
  author = {Tristan Humbert},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.29188},
  eprint = {2609.29188},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29188},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Local unmarked length spectrum rigidity for hyperbolic surfaces
AU  - Tristan Humbert
PY  - 2026
DA  - 2026/10/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.29188
UR  - https://arxiv.org/abs/2609.29188
AB  - Let (M,g) be a closed negatively curved surface. If g is strictly 1/9-pinched and has the same unmarked length spectrum as a hyperbolic metric, we show that g is hyperbolic. As a consequence, we show that any hyperbolic metric on a surface admits a C^2-neighborhood in the space of metrics in which it is characterized by its unmarked length spectrum, up to isometry.
ER  -