Results 1 to 10 of about 12,319,056 (272)

Multicomplexes on Carnot Groups and Their Associated Spectral Sequence. [PDF]

J Geom Anal, 2023
The aim of this paper is to give a thorough insight into the relationship between the Rumin complex on Carnot groups and the spectral sequence obtained from the filtration on forms by homogeneous weights that computes the de Rham cohomology of the ...
Lerario A, Tripaldi F.
europepmc   +7 more sources

On rectifiable measures in Carnot groups: representation. [PDF]

Calc Var Partial Differ Equ, 2022
AbstractThis paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of $$\mathscr {P}$$ P -rectifiable measure. First, we show that in arbitrary Carnot groups the natural infinitesimal definition of rectifiabile measure, i.e., the definition given in ...
Antonelli G, Merlo A.
europepmc   +8 more sources

Viscosity convex functions on Carnot groups [PDF]

arXiv, 2003
We prove that any locally bounded from below, upper semicontinuous v-convex function in any Carnot group is h-convex.
Changyou Wang
arxiv   +6 more sources

A notion of rectifiability modeled on Carnot groups [PDF]

Indiana University Mathematics Journal, 2000
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.
Scott D. Pauls
core   +9 more sources

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

Invertible Carnot Groups [PDF]

Analysis and Geometry in Metric Spaces, 2014
We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity.
Freeman David M.
doaj   +3 more sources

Geometric inequalities in Carnot groups [PDF]

Pacific Journal of Mathematics, 2012
Let $\GG$ be a sub-Riemannian $k$-step Carnot group of homogeneous dimension $Q$. In this paper, we shall prove several geometric inequalities concerning smooth hypersurfaces (i.e.
Montefalcone, Francescopaolo
core   +4 more sources

A metric characterization of Carnot groups [PDF]

Proceedings of the American Mathematical Society, 2014
We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically ...
Donne, Enrico Le
core   +3 more sources

Convex Hull Property and Exclosure Theorems for H-Minimal Hypersurfaces in Carnot Groups [PDF]

Analysis and Geometry in Metric Spaces, 2016
In this paper, we generalize to sub-Riemannian Carnot groups some classical results in the theory of minimal submanifolds. Our main results are for step 2 Carnot groups.
Montefalcone Francescopaolo
doaj   +3 more sources

On the H.-Q. Li inequality on step-two Carnot groups

Comptes Rendus. Mathématique, 2023
In this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. We also establish the Riemannian counterpart of the H.-Q.
Zhang, Ye
doaj   +2 more sources