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PreprintCC BY 4.0arXiv

Ergodicity of the geodesic flow on surfaces of nonpositive curvature

  • Federico Rodriguez Hertz
  • Jana Rodriguez Hertz
  • Weisheng Wu
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Abstract

We give a full proof that the geodesic flow of a closed surface of genus at least two with a C3+Lip metric of nonpositive curvature is ergodic with respect to Liouville measure. In a forthcoming paper, we will present the corresponding result for smooth rank-one manifolds in every dimension.

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Cite

BibTeXRIS
BibTeX
@misc{hertz2026ergodicity,
  title = {{Ergodicity of the geodesic flow on surfaces of nonpositive curvature}},
  author = {Federico Rodriguez Hertz and Jana Rodriguez Hertz and Weisheng Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27697},
  eprint = {2610.27697},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27697},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Ergodicity of the geodesic flow on surfaces of nonpositive curvature
AU  - Federico Rodriguez Hertz
AU  - Jana Rodriguez Hertz
AU  - Weisheng Wu
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27697
UR  - https://arxiv.org/abs/2610.27697
AB  - We give a full proof that the geodesic flow of a closed surface of genus at least two with a C^3+Lip metric of nonpositive curvature is ergodic with respect to Liouville measure. In a forthcoming paper, we will present the corresponding result for smooth rank-one manifolds in every dimension.
ER  -