Results 1 to 10 of about 12,218,361 (242)
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
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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
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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
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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 +4 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
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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
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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 ...
Antonelli, Gioacchino, Merlo, Andrea
arxiv +7 more sources
Analysis and Geometry in Metric Spaces, 2018 Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance.
Le Donne Enrico
doaj +5 more sources
Multicomplexes on Carnot Groups and Their Associated Spectral Sequence. [PDF]
J Geom Anal, 2023 AbstractThe 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 underlying group.
Lerario A, Tripaldi F.
europepmc +5 more sources
A sufficient condition for nonrigidity of Carnot groups [PDF]
Mathematische Zeitschrift, 2018 In this article we consider contact mappings on Carnot groups. Namely, we are interested in those mappings whose differential preserves the horizontal space, defined by the first stratum of the natural stratification of the Lie algebra of a Carnot group.
Ottazzi, Alessandro
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