In this paper, we aim at identifying the level sets of the gauge norm in the Heisenberg group H (n) via the prescription of their (non-constant) horizontal mean curvature. We establish a uniqueness result in H-1 under an assumption on the location of the singular set, and in H (n) for n >= 2 in the proper class of horizontally umbilical hypersurfaces.
Guidi C., Martino V., Tralli G. (2024). A characterization of gauge balls in ℍⁿ by horizontal curvature. ADVANCES IN CALCULUS OF VARIATIONS, 17(3), 753-774 [10.1515/acv-2022-0058].
A characterization of gauge balls in ℍⁿ by horizontal curvature
Martino V.;
2024
Abstract
In this paper, we aim at identifying the level sets of the gauge norm in the Heisenberg group H (n) via the prescription of their (non-constant) horizontal mean curvature. We establish a uniqueness result in H-1 under an assumption on the location of the singular set, and in H (n) for n >= 2 in the proper class of horizontally umbilical hypersurfaces.File in questo prodotto:
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