Affiliation:
1. CNRS , Institut Fourier , Université Grenoble Alpes , F-38000 Grenoble , France ; and SISSA, Via Bonomea, 265, 34136 Trieste, Italy
Abstract
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 paper is the introduction of a concept of a 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 and Nhieu in
[D. Danielli, N. Garofalo and D. M. Nhieu,
Integrability of the sub-Riemannian mean curvature of surfaces in the Heisenberg group,
Proc. Amer. Math. Soc. 140 2012, 3, 811–821],
proving that the mean curvature of a real-analytic surface with discrete characteristic set is locally integrable.
Subject
Applied Mathematics,Analysis
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