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arXiv · 2010.03480

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

Tommaso Rossi
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Abstract

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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Tommaso Rossi. 2020-10-07. Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group. https://arxiv.org/abs/2010.03480

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