A characterization of gauge balls in $\mathbb{H}^n$ by horizontal curvature

Chiara Guidi; Vittorio Martino; Giulio Tralli

A characterization of gauge balls in $\mathbb{H}^n$ by horizontal curvature

Differential Geometry 2022-07-06 v1

Authors: Chiara Guidi , Vittorio Martino , Giulio Tralli

Abstract

In this paper we aim at identifying the level sets of the gauge norm in the Heisenberg group $\mathbb{H}^n$ via the prescription of their (non-constant) horizontal mean curvature. We establish a uniqueness result in $\mathbb{H}^1$ under an assumption on the location of the singular set, and in $\mathbb{H}^n$ for $n\geq 2$ in the proper class of horizontally umbilical hypersurfaces

Keywords

heisenberg group gauge norm horizontal mean curvature uniqueness horizontally umbilical hypersurfaces

Cite

@article{arxiv.2207.02181,
  title  = {A characterization of gauge balls in $\mathbb{H}^n$ by horizontal curvature},
  author = {Chiara Guidi and Vittorio Martino and Giulio Tralli},
  journal= {arXiv preprint arXiv:2207.02181},
  year   = {2022}
}

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