Nowhere differentiable intrinsic Lipschitz graphs
Julia, A., Nicolussi Golo, S., & Vittone, D. (2021). Nowhere differentiable intrinsic Lipschitz graphs. Bulletin of the London Mathematical Society, Early View. https://doi.org/10.1112/blms.12540
Published inBulletin of the London Mathematical Society
© 2021 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.
We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneous subgroup. This provides counterexamples to a Rademacher theorem for intrinsic Lipschitz graphs.
Publication in research information system
MetadataShow full item record
Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF
Additional information about fundingAJ has been supported by the Simons Foundation Wave Project. SNG has been supported by the Academy of Finland (grant 322898 ‘Sub-Riemannian Geometry via Metric-geometry and Lie-group Theory'). DV has been supported by FFABR 2017 of MIUR (Italy) and by GNAMPA of INdAM (Italy). All three authors have been supported by the University of Padova STARS Project ‘Sub-Riemannian Geometry and Geometric Measure Theory Issues: Old and New’ ...
Showing items with similar title or keywords.
Antonelli, Gioacchino; Le Donne, Enrico (Elsevier, 2020)This paper is related to the problem of finding a good notion of rectifiability in sub-Riemannian geometry. In particular, we study which kind of results can be expected for smooth hypersurfaces in Carnot groups. Our main ...
Fässler, Katrin; Le Donne, Enrico (Springer, 2021)This note is concerned with the geometric classification of connected Lie groups of dimension three or less, endowed with left-invariant Riemannian metrics. On the one hand, assembling results from the literature, we give ...
Le Donne, Enrico; Moisala, Terhi (Springer, 2021)This paper contributes to the study of sets of finite intrinsic perimeter in Carnot groups. Our intent is to characterize in which groups the only sets with constant intrinsic normal are the vertical half-spaces. Our ...
Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups Di Donato, Daniela; Fässler, Katrin (Springer, 2021)This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group Hn, n∈N. For 1⩽k⩽n, we show that every intrinsic L-Lipschitz graph over a subset ...
A Primer on Carnot Groups: Homogenous Groups, Carnot-Carathéodory Spaces, and Regularity of Their Isometries Le Donne, Enrico (De Gruyter Open, 2017)Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with ...