Results 11 to 20 of about 12,258,354 (255)

On Rectifiable Measures in Carnot Groups: Existence of Density. [PDF]

J Geom Anal, 2022
AbstractIn this paper, we start a detailed study of a new notion of rectifiability in Carnot groups: we say that a Radon measure is$${\mathscr {P}}_h$$Ph-rectifiable, for$$h\in {\mathbb {N}}$$h∈N, if it has positiveh-lower density and finiteh-upper density almost everywhere, and, at almost every point, it admits a unique tangent measure up to multiples.
Antonelli G, Merlo A.
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About coincidence points theorems on 2-step Carnot groups with 1-dimensional centre equipped with Box-quasimetrics

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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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
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The Fractional Powers of the Sub-Laplacian in Carnot Groups Through an Analytic Continuation [PDF]

Journal of Geometric Analysis, 2023
In this paper we construct the fractional powers of the sub-Laplacian in Carnot groups through an analytic continuation approach. In addition, we characterize the powers of the fractional sub-Laplacian in the Heisenberg group, and as a byproduct we ...
Francesca Corni, Fausto Ferrari
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Viscosity convex functions on Carnot groups [PDF]

Proceedings of the American Mathematical Society, 2003
We prove that any upper semicontinuous v-convex function in any Carnot group is h-convex.
Changyou Wang
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A notion of rectifiability modeled on Carnot groups [PDF]

Indiana University Mathematics Journal, 2000
27 ...
Scott D. Pauls
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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
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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
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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
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Hausdorff measure of the singular set of quasiregular maps on Carnot groups [PDF]

International Journal of Mathematics and Mathematical Sciences, 2003
Irina Markina
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