Results 31 to 40 of about 535 (65)

Riemannian and Sub-Riemannian geodesic flows

, 2015
In the present paper we show that the geodesic flows of a sub-Riemannian metric and that of a Riemannian extension commute if and only if the extended metric is parallel with respect to a certain connection. This helps us to describe the geodesic flow of
Grong, Erlend, Molina, Mauricio Godoy
core   +1 more source

BiLipschitz Decomposition of Lipschitz Maps between Carnot Groups

Analysis and Geometry in Metric Spaces, 2015
Let f : G → H be a Lipschitz map between two Carnot groups. We show that if B is a ball of G, then there exists a subset Z ⊂ B, whose image in H under f has small Hausdorff content, such that B\Z can be decomposed into a controlled number of pieces, the ...
Li Sean
doaj   +1 more source

Analytic torsion of nilmanifolds with (2, 3, 5) distributions

Analysis and Geometry in Metric Spaces
We consider generic rank two distributions on five-dimensional nilmanifolds and show that the analytic torsion of their Rumin complex coincides with the Ray-Singer torsion.
Haller Stefan
doaj   +1 more source

Rigidity of fiber-preserving quasisymmetric maps

, 2015
We show that fiber-preserving quasisymmetric maps are biLipschitz. As an application, we show that quasisymmetric maps on Carnot groups with reducible first stratum are ...
Donne, Enrico Le, Xie, Xiangdong
core   +1 more source

Invertible Carnot Groups [PDF]

, 2016
We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the $J^2$-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity.
Freeman, David M.
core  

Quasiconformal mappings on the Grushin plane

, 2017
We prove that a self-homeomorphism of the Grushin plane is quasisymmetric if and only if it is metrically quasiconformal and if and only if it is geometrically quasiconformal.
Gartland, Chris, Jung, Derek, Romney, Matthew   +2 more
core   +1 more source

On tangent cones to length minimizers in Carnot-Carath\'eodory spaces

, 2017
We give a detailed proof of some facts about the blow-up of horizontal curves in Carnot-Carath\'eodory spaces.Comment: 19 ...
Monti, Roberto, Pigati, Alessandro, Vittone, Davide   +2 more
core   +1 more source

Curvature exponent and geodesic dimension on Sard-regular Carnot groups

Analysis and Geometry in Metric Spaces
In this study, we characterize the geodesic dimension NGEO{N}_{{\rm{GEO}}} and give a new lower bound to the curvature exponent NCE{N}_{{\rm{CE}}} on Sard-regular Carnot groups.
Golo Sebastiano Nicolussi, Zhang Ye
doaj   +1 more source

Partial Isometries of a Sub-Riemannian Manifold

, 2012
In this paper, we obtain the following generalisation of isometric $C^1$-immersion theorem of Nash and Kuiper. Let $M$ be a smooth manifold of dimension $m$ and $H$ a rank $k$ subbundle of the tangent bundle $TM$ with a Riemannian metric $g_H$.
Eliashberg Y., Kuiper N. H., MAHUYA DATTA, Spring D.   +3 more
core   +1 more source

On an evolution equation in sub-Finsler geometry

Analysis and Geometry in Metric Spaces
We study the gradient flow of an energy with mixed homogeneity, which is at the interface of Finsler and sub-Riemannian geometry.
Garofalo Nicola
doaj   +1 more source