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The Sharp Isoperimetric Inequality in the First Heisenberg Group
Abstract
We prove the sharp horizontal isoperimetric inequality in the first Heisenberg group for all sets of finite horizontal perimeter and positive finite volume, with equality precisely for left translates and dilates of the Pansu ball.
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BibTeX
@misc{chen2026sharp,
title = {{The Sharp Isoperimetric Inequality in the First Heisenberg Group}},
author = {Wei-Chun Chen and Wei-Ting Kao and Chun-Kai Lien},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07632},
eprint = {2610.07632},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07632},
}
RIS
TY - UNPB
TI - The Sharp Isoperimetric Inequality in the First Heisenberg Group
AU - Wei-Chun Chen
AU - Wei-Ting Kao
AU - Chun-Kai Lien
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07632
UR - https://arxiv.org/abs/2610.07632
AB - We prove the sharp horizontal isoperimetric inequality in the first Heisenberg group for all sets of finite horizontal perimeter and positive finite volume, with equality precisely for left translates and dilates of the Pansu ball.
ER -