Nilpotent Groups and Bi-Lipschitz Embeddings Into L1

Autor: Sylvester Eriksson-Bique, Chris Gartland, Enrico Le Donne, Lisa Naples, Sebastiano Nicolussi Golo

Publikováno v: International Mathematics Research Notices.

We prove that if a simply connected nilpotent Lie group quasi-isometrically embeds into an $L^1$ space, then it is abelian. We reach this conclusion by proving that every Carnot group that bi-Lipschitz embeds into $L^1$ is abelian. Our proof follows

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::ec277afff3bdee703208373d1a0c2787
https://doi.org/10.1093/imrn/rnac264

Toward a quasi-Möbius characterization of invertible homogeneous metric spaces

Autor: Enrico Le Donne, David M. Freeman

Publikováno v: Revista Matemática Iberoamericana. 37:671-722

We study locally compact metric spaces that enjoy various forms of homogeneity with respect to Mobius self-homeomorphisms. We investigate connections between such homogeneity and the combination of isometric homogeneity with invertibility. In particu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::1caa82b6457376a927bfffc8d1fa34a2
https://doi.org/10.4171/rmi/1211

Lipschitz Carnot-Carathéodory Structures and their Limits

Autor: Gioacchino Antonelli, Enrico Le Donne, Sebastiano Nicolussi Golo

In this paper we discuss the convergence of distances associated to converging structures of Lipschitz vector fields and continuously varying norms on a smooth manifold. We prove that, under a mild controllability assumption on the limit vector-field

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::964af19943f521cb2dc17430c33c083f
http://urn.fi/URN:NBN:fi:jyu-202301111268

A Cornucopia of Carnot groups in Low Dimensions

Autor: Enrico Le Donne, Francesca Tripaldi

Publikováno v: Le Donne, Enrico; Tripaldi, Francesca (2022). A Cornucopia of Carnot Groups in Low Dimensions. Analysis and geometry in metric spaces, 10(1), pp. 155-289. De Gruyter 10.1515/agms-2022-0138

Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating. When a stratified group is equipped with a left-invariant path distance that is homogeneous wi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::309fe2ee183838a0561f37a6278ac892
http://arxiv.org/abs/2008.12356

Conformal equivalence of visual metrics in pseudoconvex domains

Autor: Luca Capogna, Enrico Le Donne

Publikováno v: Mathematische Annalen

We refine estimates introduced by Balogh and Bonk, to show that the boundary extensions of isometries between smooth strongly pseudoconvex domains in $\C^n$ are conformal with respect to the sub-Riemannian metric induced by the Levi form. As a coroll

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f005493d3b768d69e9a41bf96f2c45b6