Results 21 to 30 of about 505 (56)

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   +2 more sources

Uniform Gaussian Bounds for Subelliptic Heat Kernels and an Application to the Total Variation Flow of Graphs over Carnot Groups

Analysis and Geometry in Metric Spaces, 2013
In this paper we study heat kernels associated with a Carnot group G, endowed with a family of collapsing left-invariant Riemannian metrics σε which converge in the Gromov- Hausdorff sense to a sub-Riemannian structure on G as ε→ 0.
Capogna Luca, Citti Giovanna, Manfredini Maria   +2 more
doaj   +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

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

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

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

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

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