Rank-one theorem and subgraphs of BV functions in Carnot groups

DOI10.1016/j.jfa.2018.09.016zbMath1410.49052arXiv1712.02242OpenAlexW2963289585WikidataQ129105991 ScholiaQ129105991MaRDI QIDQ1634590

Davide Vittone, Annalisa Massaccesi, Sebastiano Don

Publication date: 18 December 2018

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.02242

zbMATH Keywords

sub-Riemannian geometryCarnot groupsfunctions with bounded variationrank-one theorem

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Length, area, volume, other geometric measure theory (28A75)

Related Items (10)

A rectifiability result for finite-perimeter sets in Carnot groups ⋮ Area of intrinsic graphs and coarea formula in Carnot groups ⋮ BV spaces and the perimeters related to Schrödinger operators with inverse-square potentials and applications to the rank-one theorem ⋮ Intrinsic rectifiability via flat cones in the Heisenberg group ⋮ Subgraphs of \(\alpha\)-Hermite BV functions and the rank-one theorem for \(\mathcal{BV}_{\mathcal{H}_{\alpha}}\) ⋮ Subgraphs of BV functions on RCD spaces ⋮ Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces ⋮ Fine properties of functions with bounded variation in Carnot-Carathéodory spaces ⋮ An elementary proof of the rank-one theorem for BV functions ⋮ Lipschitz graphs and currents in Heisenberg groups

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