Results 31 to 40 of about 496 (56)

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  

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 the role of embeddability in conformal pseudo-hermitian geometry

Analysis and Geometry in Metric Spaces
In this article, we review some recent results about the role of embeddability in conformal CR (Cauchy-Riemann) geometry. We will show how this condition enters in the second variation of the pseudo-hermitian counterpart of the Einstein-Hilbert action ...
Malchiodi Andrea
doaj   +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

Comparing three possible hypoelliptic Laplacians on the 5-dimensional Cartan group via div-curl type estimates

Advanced Nonlinear Studies
On general Carnot groups, the definition of a possible hypoelliptic Hodge-Laplacian on forms using the Rumin complex has been considered in (M. Rumin, “Differential geometry on C-C spaces and application to the Novikov-Shubin numbers of nilpotent Lie ...
Baldi Annalisa, Tripaldi Francesca
doaj   +1 more source

Superintegrability of Sub-Riemannian Problems on Unimodular 3D Lie Groups [PDF]

, 2014
Left-invariant sub-Riemannian problems on unimodular 3D Lie groups are considered. For the Hamiltonian system of Pontryagin maximum principle for sub-Riemannian geodesics, the Liouville integrability and superintegrability are ...
Mashtakov, Alexey P., Sachkov, Yuri L.
core   +1 more source

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

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