Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group - Archive ouverte HAL
Article Dans Une Revue Advances in Calculus of Variation Année : 2021

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

Tommaso Rossi
  • Fonction : Auteur

Résumé

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 [DGN12], proving that the mean curvature of a real-analytic surface with discrete characteristic set is locally integrable.
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Dates et versions

hal-02960528 , version 1 (07-10-2020)

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Tommaso Rossi. Integrability of the sub-Riemannian mean curvature at degenerate characteristic points in the Heisenberg group. Advances in Calculus of Variation, 2021, 16 (1), pp.99-110. ⟨10.1515/acv-2020-0098⟩. ⟨hal-02960528⟩
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