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• W2240485153 abstract "We study left-invariant distances on Lie groups for which there exists a one-parameter family of homothetic automorphisms. The main examples are Carnot groups, in particular the Heisenberg group with the standard dilations. We are interested in criteria implying that, locally and away from the diagonal, the distance is Euclidean Lipschitz and, consequently, that the metric spheres are boundaries of Lipschitz domains in the Euclidean sense. In the first part of the paper, we consider geodesic distances. In this case, we actually prove the regularity of the distance in the more general context of sub-Finsler manifolds with no abnormal geodesics. Secondly, for general groups we identify an algebraic criterium in terms of the dilating automorphisms, which for example makes us conclude the regularity of homogeneous distances on the Heisenberg this http URL such a group, we analyze in more details the geometry of metric spheres. We also provide examples of homogeneous groups where spheres presents cusps." @default.
• W2240485153 created "2016-06-24" @default.
• W2240485153 creator A5028748648 @default.
• W2240485153 creator A5086260956 @default.
• W2240485153 date "2015-09-13" @default.
• W2240485153 modified "2023-09-27" @default.
• W2240485153 title "Regularity properties of spheres in homogeneous groups" @default.
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