Calculus of Variations and Geometric Measure Theory
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T. Rossi

Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group

created by rossi1 on 08 Oct 2020
modified on 11 Oct 2021


Published Paper

Inserted: 8 oct 2020
Last Updated: 11 oct 2021

Journal: Advances in Calculus of Variations
Year: 2021

ArXiv: 2010.03480 PDF


We address the problem of integrability of the sub-Riemannian mean curvature of an embedded hypersurface around isolated characteristic points. The main contribution of this note is the introduction of a concept of mildly degenerate characteristic point for a smooth surface of the Heisenberg group, in a neighborhood of which the sub-Riemannian mean curvature is integrable (with respect to the perimeter measure induced by the Euclidean structure). As a consequence we partially answer to a question posed by Danielli-Garofalo-Nhieu in Danielli D., Garofalo N., Nhieu D.M., Proc. Amer. Math. Soc., 2012, proving that the mean curvature of a real-analytic surface with discrete characteristic set is locally integrable.

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