Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 59 min ago
PreprintCC BY 4.0arXiv

A Proof of the Analytic Entropy Conjecture

  • Xiaoyang Chen
  • Xiang Jiang
Open at sourcePDFDOICite

Abstract

We prove that the geodesic flow of a closed real-analytic Riemannian manifold has zero topological entropy if it admits globally defined, real-analytic Liouville integrals. This proves a longstanding conjecture proposed by Bolsinov and Taimanov.

Related

  1. A requested analytic proof of an identity of Dixit, Kumar, and Srivastava
    Philip Cuthbertson
    arXivPreprintarXiv licenceFull textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  2. Analytic Liouville Integrable Geodesic Flow Has Zero Entropy
    Fei Liu, Xiaokai Liu, Xiang Zhang
    arXivPreprintCC BY 4.0Full textDynamical systemsGeometry & topologyarXiv
  3. A proof of the Stanley-Stembridge conjecture
    Tatsuyuki Hikita
    Journal of the American Mathematical SocietyPeer-reviewedLicence not statedFull text51 citedCombinatorics & discrete mathematicsOpenAlex
  4. A streamlined proof of the Kakeya set conjecture in R3
    Larry Guth, Hong Wang, Joshua Zahl
    MathematikaPeer-reviewedLicence not statedFull text12 citedGeneral mathematicsOpenAlex
  5. A proof of Alexander’s Conjecture on an Inequality of Cassels
    Myriam Ounaïes
    Complex Analysis and Operator TheoryPeer-reviewedLicence not statedFull textGeometry & topologyHAL

Cite

BibTeXRIS
BibTeX
@misc{chen2026proof,
  title = {{A Proof of the Analytic Entropy Conjecture}},
  author = {Xiaoyang Chen and Xiang Jiang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.14065},
  eprint = {2610.14065},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.14065},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Proof of the Analytic Entropy Conjecture
AU  - Xiaoyang Chen
AU  - Xiang Jiang
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.14065
UR  - https://arxiv.org/abs/2610.14065
AB  - We prove that the geodesic flow of a closed real-analytic Riemannian manifold has zero topological entropy if it admits globally defined, real-analytic Liouville integrals. This proves a longstanding conjecture proposed by Bolsinov and Taimanov.
ER  -