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arXiv · 2207.02181

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

Chiara Guidi·Vittorio Martino·Giulio Tralli
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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

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Chiara Guidi, Vittorio Martino, Giulio Tralli. 2022-07-05. A characterization of gauge balls in $\mathbb{H}^n$ by horizontal curvature. https://arxiv.org/abs/2207.02181

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