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A semi-discrete scheme for horizontal mean curvature flow in the Heisenberg group

  • A. Cesaroni
  • M. Novaga
  • P. Pozzi
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Abstract

The horizontal mean curvature flow is a geometric evolution associated with the horizontal perimeter in sub-Riemannian spaces. In this paper, we introduce a minimizing movement scheme for this flow in the first Heisenberg group ℍ, and prove the existence of a flat flow which is locally 1/2-Hölder continuous in time, with respect to the L1-distance. The construction applies to arbitrary bounded sets of finite horizontal perimeter and does not require smoothness or symmetry of the initial datum.

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Cite

BibTeXRIS
BibTeX
@misc{cesaroni2026semidiscrete,
  title = {{A semi-discrete scheme for horizontal mean curvature flow in the Heisenberg group}},
  author = {A. Cesaroni and M. Novaga and P. Pozzi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.20054},
  eprint = {2610.20054},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.20054},
}
RIS
TY  - UNPB
TI  - A semi-discrete scheme for horizontal mean curvature flow in the Heisenberg group
AU  - A. Cesaroni
AU  - M. Novaga
AU  - P. Pozzi
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.20054
UR  - https://arxiv.org/abs/2610.20054
AB  - The horizontal mean curvature flow is a geometric evolution associated with the horizontal perimeter in sub-Riemannian spaces. In this paper, we introduce a minimizing movement scheme for this flow in the first Heisenberg group ℍ, and prove the existence of a flat flow which is locally 1/2-Hölder continuous in time, with respect to the L^1-distance. The construction applies to arbitrary bounded sets of finite horizontal perimeter and does not require smoothness or symmetry of the initial datum.
ER  -