Skip to content
DraconiticResearch
Search Sources API
178,970 studies31 sourcesUpdated 26 min ago
PreprintarXiv licencearXiv

On local minimality of Hausdorff dimension for round limit sets

  • Sami Douba
  • Andrés Sambarino
  • Franco Vargas Pallete
Open at sourcePDFDOICite

Abstract

We address a question of Canary--Taylor and Canary--Minsky--Taylor for sufficiently symmetric compact hyperbolic $3$-orbifolds with totally geodesic boundary. We give sufficient conditions on the symmetries of such an orbifold to show that, among the complete convex cocompact structures on the interior, the structure with Fuchsian ends is a critical point (respectively, a strict local minimum) for the critical exponent. We also provide an infinite family of non-rigid examples fulfilling these conditions.

Related

  1. Valeur exacte de la mesure de Hausdorff d'un sous-ensemble fractal de dimension log 3 / log 4 du triangle de Sierpinski
    Jacques Marion
    HALPreprintLicence Ouverte 2.0Full textGeometry & topologyHAL
  2. Effective Hausdorff dimension one is cofinal in the K-degrees
    Xuanheng Zhao
    arXivPreprintCC BY 4.0Full textLogic & foundationsarXiv
  3. On the Hausdorff dimension of oscillatory motions in three-body problems
    Anton Gorodetski, Vadim Kaloshin
    arXivPreprintarXiv licenceFull textDynamical systemsarXiv
  4. Hausdorff dimension of the singular set in optimal transport
    Shibing Chen, Qi-Rui Li, Yuanyuan Li +2
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv
  5. New bound on the Hausdorff dimension of Kakeya sets in ℝ4
    Mukul Rai Choudhuri
    arXivPreprintCC BY 4.0Full textAnalysis & PDEsarXiv

Cite

BibTeXRIS
BibTeX
@misc{douba2026local,
  title = {{On local minimality of Hausdorff dimension for round limit sets}},
  author = {Sami Douba and Andrés Sambarino and Franco Vargas Pallete},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20358},
  eprint = {2610.20358},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20358},
}
RIS
TY  - UNPB
TI  - On local minimality of Hausdorff dimension for round limit sets
AU  - Sami Douba
AU  - Andrés Sambarino
AU  - Franco Vargas Pallete
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.20358
UR  - https://arxiv.org/abs/2610.20358
AB  - We address a question of Canary--Taylor and Canary--Minsky--Taylor for sufficiently symmetric compact hyperbolic $3$-orbifolds with totally geodesic boundary. We give sufficient conditions on the symmetries of such an orbifold to show that, among the complete convex cocompact structures on the interior, the structure with Fuchsian ends is a critical point (respectively, a strict local minimum) for the critical exponent. We also provide an infinite family of non-rigid examples fulfilling these conditions.
ER  -