Results 1 to 10 of about 12,322,898 (284)
A notion of rectifiability modeled on Carnot groups [PDF]
Indiana University Mathematics Journal, 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 +9 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
On rectifiable measures in Carnot groups: representation [PDF]
arXiv, 2021 This paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of $\mathscr{P}$-rectifiable measure. First, we show that in arbitrary Carnot groups the natural \textit{infinitesimal} definition of rectifiabile measure, i.e., the definition given in terms of the existence of \textit{flat ...
Gioacchino Antonelli, Andrea Merlo
arxiv +8 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
Measure contraction properties of Carnot groups [PDF]
Calculus of Variations and Partial Differential Equations, 2016 We prove that any corank 1 Carnot group of dimension $k+1$ equipped with a left-invariant measure satisfies the $\mathrm{MCP}(K,N)$ if and only if $K \leq 0$ and $N \geq k+3$.
Rizzi, Luca
core +10 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
Sharp measure contraction property for generalized H-type Carnot groups [PDF]
Communications in Contemporary Mathematics, Vol. 20, No. 6 (2018)
1750081 (24 pages), 2017 We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group. The same result holds true for the larger class of generalized H-type Carnot groups introduced in this paper, and for which we ...
Bonfiglioli A. +4 more
arxiv +5 more sources
A Cornucopia of Carnot Groups in Low Dimensions
Analysis and Geometry in Metric Spaces, 2022 Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating.
Le Donne Enrico, Tripaldi Francesca
doaj +5 more sources
Isodiametric inequality in Carnot groups
Annales Academiae Scientiarum Fennicae Mathematica, 2010 The classical isodiametric inequality in the Euclidean space says that balls maximize the volume among all sets with a given diameter. We consider in this paper the case of Carnot groups.
Rigot, Severine
core +5 more sources
A note on lifting of Carnot groups
Revista Matemática Iberoamericana, 2005 We prove that every homogeneous Carnot group can be lifted to a free homogeneous Carnot group. Though following the ideas of Rothschild and Stein, we give simple and self-contained arguments, providing a constructive proof, as shown in the examples.
Andrea Bonfiglioli, Francesco Uguzzoni
openalex +7 more sources