Regularity of sets with constant intrinsic normal in a class of Carnot groups

DOI10.5802/aif.2853zbMath1310.28003arXiv1201.3277OpenAlexW2963280807MaRDI QIDQ486759

Marco Marchi

Publication date: 16 January 2015

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.3277

zbMATH Keywords

Carnot groupsintrinsic perimeterintrinsic rectifiability

Mathematics Subject Classification ID

Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Integration on manifolds; measures on manifolds (58C35) Length, area, volume, other geometric measure theory (28A75)

Related Items (12)

Universal differentiability sets and maximal directional derivatives in Carnot groups ⋮ Rank-one theorem and subgraphs of BV functions in Carnot groups ⋮ Semigenerated Carnot algebras and applications to sub-Riemannian perimeter ⋮ Fractional differential operators, fractional Sobolev spaces and fractional variation on homogeneous Carnot groups ⋮ Distributional solutions of Burgers' type equations for intrinsic graphs in Carnot groups of step 2 ⋮ Surface measure on, and the local geometry of, sub-Riemannian manifolds ⋮ Monotone sets and local minimizers for the perimeter in Carnot groups ⋮ Precisely monotone sets in step-2 rank-3 Carnot algebras ⋮ Marstrand-Mattila rectifiability criterion for 1-codimensional measures in Carnot groups ⋮ Differentiability and approximate differentiability for intrinsic Lipschitz functions in Carnot groups and a Rademacher theorem ⋮ Fine properties of functions with bounded variation in Carnot-Carathéodory spaces ⋮ Local minimizers and gamma-convergence for nonlocal perimeters in Carnot groups

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