Results 41 to 50 of about 14,219 (239)
AIMS Mathematics, 2023 For some class of 2-step Carnot groups $ D_n $ with 1-dimensional centre we find the exact values of the constants in $ (1, q_2) $-generalized triangle inequality for their $ \text{Box} $-quasimetrics $ \rho_{\text{Box}_{D_n}} $. Using this result we get
Alexander Greshnov, Vladimir Potapov
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A sufficient condition for nonrigidity of Carnot groups [PDF]
Mathematische Zeitschrift, 2007 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.
Alessandro Ottazzi, Alessandro Ottazzi
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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
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Quasisymmetric maps of boundaries of amenable hyperbolic groups [PDF]
, 2014 In this paper we show that if $Y=N \times \mathbb{Q}_m$ is a metric space where $N$ is a Carnot group endowed with the Carnot-Caratheodory metric then any quasisymmetric map of $Y$ is actually bilipschitz. The key observation is that $Y$ is the parabolic
Dymarz, Tullia
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Sard Property for the endpoint map on some Carnot groups [PDF]
, 2015 In Carnot-Caratheodory or sub-Riemannian geometry, one of the major open problems is whether the conclusions of Sard's theorem holds for the endpoint map, a canonical map from an infinite-dimensional path space to the underlying finite-dimensional ...
Donne, Enrico Le +4 more
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Nonlocal diffusion equations in Carnot groups
Rendiconti del Circolo Matematico di Palermo Series 2, 2022 Let $G$ be a Carnot group. We study nonlocal diffusion equations in a domain $ $ of $G$ of the form $$ u_t^ (x,t)=\int_{G}\frac{1}{ ^2}K_ (x,y)(u^ (y,t)-u^ (x,t))\,dy, \qquad x\in $$ with $u^ =g(x,t)$ for $x\notin $. For appropriate rescaled kernel $K_ $ we prove that solutions $u^ $, when $ \rightarrow0$, uniformly approximate the ...
Isolda E. Cardoso, Raúl E. Vidal
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Intrinsic regular surfaces in Carnot groups
Bruno Pini Mathematical Analysis SeminarA Carnot group $G$ is a simply connected, nilpotent Lie group with stratified Lie algebra. Intrinsic regular surfaces in Carnot groups play the same role as C1 surfaces in Euclidean spaces.
Daniela Di Donato
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The Traveling Salesman Theorem in Carnot groups [PDF]
Calculus of Variations and Partial Differential Equations, 2018 Let $\mathbb{G}$ be any Carnot group. We prove that, if a subset of $\mathbb{G}$ is contained in a rectifiable curve, then it satisfies Peter Jones' geometric lemma with some natural modifications. We thus prove one direction of the Traveling Salesman Theorem in $\mathbb{G}$.
Sean Li +2 more
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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 the codimension of the abnormal set in step two Carnot groups [PDF]
, 2018 In this article we prove that the codimension of the abnormal set of the endpoint map for certain classes of Carnot groups of step 2 is at least three.
Ottazzi, Alessandro, Vittone, Davide
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