PreprintarXiv licencearXiv
Stable Rigidity in the Heisenberg Groups
Abstract
For n≥2, we prove that the C2 boundary of a bounded nonempty open set in ℍn is volume-preserving stable if and only if it is a Pansu sphere up to left translation and Heisenberg dilation. The proof combines centre reconstruction with a volume-constrained test field derived from Pansu dilation. Consequently, every isoperimetric region admitting an open representative with C2 boundary is a Pansu ball up to these symmetries.
Related
- Quantitative Centre Rigidity under Riemannian Approximation in Heisenberg Groups
- Cohomology of annuli, duality and L∞-differential forms on Heisenberg groups
- L1-Poincar\'e inequalities for differential forms on Euclidean spaces and Heisenberg groups
- Gromov-Hausdorff Stability and Rigidity of manifolds via Heisenberg-Pauli-Weyl Uncertainty Principle
- The Isoperimetric Inequality in Higher-Dimensional Heisenberg Groups
BibTeX
@misc{chen2026stable,
title = {{Stable Rigidity in the Heisenberg Groups}},
author = {Wei-Chun Chen and Wei-Ting Kao and Chun-Kai Lien},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03900},
eprint = {2610.03900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03900},
}
RIS
TY - UNPB
TI - Stable Rigidity in the Heisenberg Groups
AU - Wei-Chun Chen
AU - Wei-Ting Kao
AU - Chun-Kai Lien
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03900
UR - https://arxiv.org/abs/2610.03900
AB - For n≥2, we prove that the C^2 boundary of a bounded nonempty open set in ℍ^n is volume-preserving stable if and only if it is a Pansu sphere up to left translation and Heisenberg dilation. The proof combines centre reconstruction with a volume-constrained test field derived from Pansu dilation. Consequently, every isoperimetric region admitting an open representative with C^2 boundary is a Pansu ball up to these symmetries.
ER -