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.

Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group / Rossi, Tommaso. - In: ADVANCES IN CALCULUS OF VARIATIONS. - ISSN 1864-8258. - 16:1(2023), pp. 99-110. [10.1515/acv-2020-0098]

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

Rossi, Tommaso
2023-01-01

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.
2023
16
1
99
110
https://arxiv.org/abs/2010.03480
Rossi, Tommaso
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/142230
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