Results 1 to 10 of about 12,282,054 (205)

Curvature exponent and geodesic dimension on Sard-regular Carnot groups [PDF]

Analysis and Geometry in Metric Spaces, 2023
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   +2 more sources

A notion of rectifiability modeled on Carnot groups [PDF]

, 2004
We introduce a notion of rectifiability modeled on Carnot groups. Precisely, we say that a subset E of a Carnot group M and N is a subgroup of M, we say E is N-rectifiable if it is the Lipschitz image of a positive measure subset of N.
Pauls, Scott D.
core   +6 more sources

On coincidence of $p$-module of a family of curves and $p$-capacity on the Carnot group

, 2003
The notion of the extremal length and the module of families of curves has been studied extensively and has given rise to a lot of applications to complex analysis and the potential theory.
Irina Markina
openalex   +3 more sources

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   +3 more sources

Review of Carnot Battery Technology Commercial Development

Energies, 2022
Carnot batteries are a quickly developing group of technologies for medium and long duration electricity storage. It covers a large range of concepts which share processes of a conversion of power to heat, thermal energy storage (i.e., storing thermal ...
Vaclav Novotny, Vit Basta, Petr Smola, Jan Spale   +3 more
doaj   +2 more sources

Escape from compact sets of normal curves in Carnot groups [PDF]

E S A I M: Control, Optimisation and Calculus of Variations, 2023
In the setting of subFinsler Carnot groups, we consider curves that satisfy the normal equation coming from the Pontryagin Maximum Principle. We show that, unless it is constant, each such a curve leaves every compact set, quantitatively.
Enrico Le Donne, Nicola Paddeu
openalex   +3 more sources

Jean-Marie Souriau’s Symplectic Foliation Model of Sadi Carnot’s Thermodynamics [PDF]

Entropy
The explanation of thermodynamics through geometric models was initiated by seminal figures such as Carnot, Gibbs, Duhem, Reeb, and Carathéodory. Only recently, however, has the symplectic foliation model, introduced within the domain of geometric ...
Frédéric Barbaresco
doaj   +2 more sources

Sharp Hardy Identities and Inequalities on Carnot Groups

Advanced Nonlinear Studies, 2021
In this paper we establish general weighted Hardy identities for several subelliptic settings including Hardy identities on the Heisenberg group, Carnot groups with respect to a homogeneous gauge and Carnot–Carathéodory metric, general nilpotent groups ...
Nguyen Lam
exaly   +2 more sources

Loomis–Whitney inequalities on corank 1 Carnot groups [PDF]

Annales Fennici Mathematici
In this paper we provide another way to deduce the Loomis–Whitney inequality on higher dimensional Heisenberg groups \(\mathbb{H}^n\) based on the one on the first Heisenberg group \(\mathbb{H}^1\) and the known nonlinear Loomis–Whitney inequality (which
Ye Zhang
openalex   +3 more sources

Non co-adapted couplings of Brownian motions on free, step 2 Carnot groups [PDF]

E S A I M: Probability & Statistics
On the free, step $2$ Carnot groups of rank $n$ $\Ge_n$, the subRiemannian Brownian motion consists in a $\mathbb{R}^n$-Brownian motion together with its $\frac{n(n-1)}{2}$ Lévy areas.
Magalie Bénéfice
openalex   +2 more sources