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PreprintarXiv licencearXiv

Fuglede's theorem in the Heisenberg group

  • Davide Massenz
  • Roberto Monti
  • Julián Pozuelo
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Abstract

We prove a Fuglede-type quantitative isoperimetric inequality for the Pansu sphere, the conjectured isoperimetric set in the sub-Riemannian Heisenberg group ℍ1. We show that, among suitable volume-preserving normal perturbations of the Pansu sphere that are small in a weighted C2-norm, the difference between the sub-Riemannian perimeters of the perturbed and unperturbed regions is bounded below by a positive constant times the square of their L1-distance. The proof is based on a Riemannian approximation argument with uniform estimates.

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Cite

BibTeXRIS
BibTeX
@misc{massenz2026fugledes,
  title = {{Fuglede's theorem in the Heisenberg group}},
  author = {Davide Massenz and Roberto Monti and Julián Pozuelo},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32393},
  eprint = {2610.32393},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32393},
}
RIS
TY  - UNPB
TI  - Fuglede's theorem in the Heisenberg group
AU  - Davide Massenz
AU  - Roberto Monti
AU  - Julián Pozuelo
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32393
UR  - https://arxiv.org/abs/2610.32393
AB  - We prove a Fuglede-type quantitative isoperimetric inequality for the Pansu sphere, the conjectured isoperimetric set in the sub-Riemannian Heisenberg group ℍ^1. We show that, among suitable volume-preserving normal perturbations of the Pansu sphere that are small in a weighted C^2-norm, the difference between the sub-Riemannian perimeters of the perturbed and unperturbed regions is bounded below by a positive constant times the square of their L^1-distance. The proof is based on a Riemannian approximation argument with uniform estimates.
ER  -