Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 40 min ago
PreprintarXiv licencearXiv

The Pu inequality and the Viterbo conjecture with finite symmetry

  • Julian Chaidez
  • Shira Tanny
Open at sourcePDFDOICite

Abstract

We study a construction for producing Finsler metrics on the sphere from convex bodies in ℝ4 using the quaternions. Among several applications, we prove the weak Viterbo conjecture for convex bodies in ℝ4 that are invariant under the natural action of the quaternion group Q. This is the first instance where Viterbo's systolic inequality is established for convex bodies with a finite group symmetry, addressing a question of Haim-Kislev-Ostrover. Moreover, a smooth Q-symmetric convex domain that achieves equality is symplectomorphic to the ball, without any assumption of strict or uniform convexity. Finally, we show that any link of minimal Reeb orbits on the boundary of a uniformly convex Q-symmetric convex body is transversely isotopic to a union of Hopf fibers, strengthening a result of Abbondandolo-Edtmair-Kang in the Q-symmetric setting.

Related

  1. A counterexample to the generalized Viterbo conjecture on the spectral distance in a disc cotangent bundle
    Filip Broćić, Baptiste Serraille, Ibrahim Trifa
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  2. A proof of Alexander’s Conjecture on an Inequality of Cassels
    Myriam Ounaïes
    Complex Analysis and Operator TheoryPeer-reviewedLicence not statedFull textGeometry & topologyHAL
  3. Symmetry breaking in the polygonal Szegö-Weinberger inequality as p→1+: the longest shortest-fence quadrilateral
    Beniamin Bogosel, Dorin Bucur, Ilaria Fragalà
    arXivPreprintCC BY-NC-ND 4.0Full textOptimisation & controlarXiv
  4. A convolution inequality and the Krzyż conjecture
    Sullivan Francis MacDonald
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  5. A Proof of Liu's Conjecture on the Fundamental Triangle Inequality
    Tserendorj Batbold
    arXivPreprintCC BY 4.0Full textGeneral mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{chaidez2026inequality,
  title = {{The Pu inequality and the Viterbo conjecture with finite symmetry}},
  author = {Julian Chaidez and Shira Tanny},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.31906},
  eprint = {2610.31906},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.31906},
}
RIS
TY  - UNPB
TI  - The Pu inequality and the Viterbo conjecture with finite symmetry
AU  - Julian Chaidez
AU  - Shira Tanny
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2610.31906
UR  - https://arxiv.org/abs/2610.31906
AB  - We study a construction for producing Finsler metrics on the sphere from convex bodies in ℝ^4 using the quaternions. Among several applications, we prove the weak Viterbo conjecture for convex bodies in ℝ^4 that are invariant under the natural action of the quaternion group Q. This is the first instance where Viterbo's systolic inequality is established for convex bodies with a finite group symmetry, addressing a question of Haim-Kislev-Ostrover. Moreover, a smooth Q-symmetric convex domain that achieves equality is symplectomorphic to the ball, without any assumption of strict or uniform convexity. Finally, we show that any link of minimal Reeb orbits on the boundary of a uniformly convex Q-symmetric convex body is transversely isotopic to a union of Hopf fibers, strengthening a result of Abbondandolo-Edtmair-Kang in the Q-symmetric setting.
ER  -