Results 21 to 30 of about 508 (56)

Nos\'e-Thermostated Mechanical Systems on the n-Torus

, 2017
Let $H(q,p) = \frac12 | p |^2 + V(q)$ be an $n$-degree of freedom $C^r$ mechanical Hamiltonian on the cotangent bundle of the $n$-torus where $r>2n+2$. When the metric $| * |$ is flat, the Nos\'e-thermostated system associated to $H$ is shown to have a ...
Butler, Leo T.
core   +1 more source

On Conditions for Unrectifiability of a Metric Space

Analysis and Geometry in Metric Spaces, 2014
We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a ...
Hajłasz Piotr, Malekzadeh Soheil
doaj   +1 more source

A counterexample to gluing theorems for MCP metric measure spaces

, 2018
Perelman's doubling theorem asserts that the metric space obtained by gluing along their boundaries two copies of an Alexandrov space with curvature $\geq \kappa$ is an Alexandrov space with the same dimension and satisfying the same curvature lower ...
Rizzi, Luca
core   +3 more sources

Metric lines in the jet space

Analysis and Geometry in Metric Spaces
In the realm of sub-Riemannian manifolds, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of kk-jets of a real function of one real variable xx, denoted by Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}),
Bravo-Doddoli Alejandro
doaj   +1 more source

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