Results 1 to 10 of about 1,129 (83)

Braided spaces with dilations and sub-riemannian symmetric spaces [PDF]

, 2011
Braided sets which are also spaces with dilations are presented and explored in this paper, in the general frame of emergent algebras arxiv:0907.1520. Examples of such spaces are the sub-riemannian symmetric spaces.
Buliga, Marius
core  

Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups $H^n, n>1$ [PDF]

arXiv, 2008
We prove that Lipschitz intrinsic graphs in the Heisenberg groups $H^n$, with $n>1$, which are vanishing viscosity solutions of the minimal surface equation are smooth.
arxiv  

Cross ratios and the Ptolemaean inequality in boundaries of symmetric spaces of rank 1 [PDF]

arXiv, 2012
We use generalised cross--ratios to prove the Ptolemaean inequality and the Theorem of Ptolemaeus in the setting of the boundary of symmetric Riemannian spaces of rank 1 and of negative curvature.
arxiv  

C1,α-rectifiability in low codimension in Heisenberg groups

Analysis and Geometry in Metric Spaces
A natural higher-order notion of C1,α{C}^{1,\alpha }-rectifiability ...
Idu Kennedy Obinna, Maiale Francesco Paolo   +1 more
doaj   +1 more source

Quasiconformal maps on non-rigid Carnot groups [PDF]

arXiv, 2013
We study quasiconformal maps on non-rigid Carnot groups equipped with Carnot metric. We show that for most non-rigid Carnot groups N, all quasiconformal maps on N must be biLipschitz.
arxiv  

Surface measure on, and the local geometry of, sub-Riemannian manifolds. [PDF]

Calc Var Partial Differ Equ, 2023
Don S, Magnani V.
europepmc   +1 more source

Numerical Methods and Closed Orbits in the Kepler-Heisenberg Problem

, 2017
The Kepler-Heisenberg problem is that of determining the motion of a planet around a sun in the sub-Riemannian Heisenberg group. The sub-Riemannian Hamiltonian provides the kinetic energy, and the gravitational potential is given by the fundamental ...
Dods, Victor, Shanbrom, Corey
core  

The topology of quaternionic contact manifolds [PDF]

arXiv, 2014
We explore the consequences of curvature and torsion on the topology of quaternionic contact manifolds with integrable vertical distribution. We prove a general Myers theorem and establish a Cartan-Hadamard result for almost qc-Einstein manifolds.
arxiv  

Almost-Riemannian manifolds do not satisfy the curvature-dimension condition. [PDF]

Calc Var Partial Differ Equ, 2023
Magnabosco M, Rossi T.
europepmc   +1 more source

Rigidity of fiber-preserving quasisymmetric maps [PDF]

arXiv, 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 biLipschitz.
arxiv