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

2020/10/07 by Tommaso Rossi, Rossi, Tommaso · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Partial Differential Equations #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2010.03480

openalex publication_date 2020/10/07 · openalex created_date 2022/08/24 · openalex updated_date 2026/07/28

Abstract

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

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