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PreprintCC BY 4.0arXiv

The Bernstein problem in higher dimensional Heisenberg groups

  • Gianmarco Giovannardi
  • Simone Verzellesi
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Abstract

In every sub-Riemannian Heisenberg group ℍn, with n≥ 2, we prove the existence of a global perimeter minimizer whose boundary is a smooth, non-characteristic, entire intrinsic graph but it is not a vertical hyperplane.

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Cite

BibTeXRIS
BibTeX
@misc{giovannardi2026bernstein,
  title = {{The Bernstein problem in higher dimensional Heisenberg groups}},
  author = {Gianmarco Giovannardi and Simone Verzellesi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13913},
  eprint = {2610.13913},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13913},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Bernstein problem in higher dimensional Heisenberg groups
AU  - Gianmarco Giovannardi
AU  - Simone Verzellesi
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13913
UR  - https://arxiv.org/abs/2610.13913
AB  - In every sub-Riemannian Heisenberg group ℍ^n, with n≥ 2, we prove the existence of a global perimeter minimizer whose boundary is a smooth, non-characteristic, entire intrinsic graph but it is not a vertical hyperplane.
ER  -