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PreprintCC BY 4.0HAL

Marked length spectrum and area of surfaces with Anosov geodesic flow

  • Marcos Cossarini
  • St Éphane Sabourau
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Abstract

More than twenty years ago, Croke and Dairbekov showed that a negatively curved metric g0 on a closed surface has minimal area among all negatively curved Riemannian metrics g on the same surface whose marked length spectrum is greater or equal to that of g0. We show that the curvature assumption on the second metric can be removed and extend this result to reversible Finsler metrics. More precisely, we prove that a reversible Finsler metric F0 on a closed surface whose geodesic flow is Anosov has minimal area among all reversible Finsler metrics F on the same surface whose marked length spectrum is greater or equal to that of F0.

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Cite

BibTeXRIS
BibTeX
@misc{cossarini2026marked,
  title = {{Marked length spectrum and area of surfaces with Anosov geodesic flow}},
  author = {Marcos Cossarini and St Éphane Sabourau},
  howpublished = {HAL},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32489},
  eprint = {2610.32489},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05837410v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Marked length spectrum and area of surfaces with Anosov geodesic flow
AU  - Marcos Cossarini
AU  - St Éphane Sabourau
PY  - 2026
DA  - 2026/10/23
PB  - HAL
DO  - 10.48550/arxiv.2610.32489
UR  - https://hal.science/hal-05837410v1
AB  - More than twenty years ago, Croke and Dairbekov showed that a negatively curved metric g0 on a closed surface has minimal area among all negatively curved Riemannian metrics g on the same surface whose marked length spectrum is greater or equal to that of g0. We show that the curvature assumption on the second metric can be removed and extend this result to reversible Finsler metrics. More precisely, we prove that a reversible Finsler metric F0 on a closed surface whose geodesic flow is Anosov has minimal area among all reversible Finsler metrics F on the same surface whose marked length spectrum is greater or equal to that of F0.
ER  -