Results 181 to 190 of about 18,179 (207)

Subharmonic functions on Carnot groups

Mathematische Annalen, 2003
The authors develop a potential theory for \(\Delta_G\)-subharmonic functions in \(\mathbb{R}^N\), where \(\Delta_G\) is the sub-Laplacian in a Carnot group \(G\). The main results are analogues to Riesz representation and Poisson-Jensen formulas, Nevanlinna type theorems, and a characterization of the \(\Delta_G\)-Riesz measures of upper bounded ...
Ermanno Lanconelli, Andrea Bonfiglioli
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Quasiregular maps on Carnot groups

Journal of Geometric Analysis, 1997
The authors develop a theory of quasiregular maps in a sub-Riemannian geometry of two-step Carnot groups. An analytic definition for quasiregularity is suggested and it is shown that conconstant quasiregular maps are open and discrete maps on Carnot groups which are two-step nilpotent and of Heisenberg type. Some results which are known to be valid in \
Juha Heinonen, Juha Heinonen, Ilkka Holopainen, Ilkka Holopainen   +3 more
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Mikhlin’s problem on Carnot groups

Siberian Mathematical Journal, 2008
Summary: We consider one class of singular integral operators over the functions on domains of Carnot groups.
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WAVE AND MAXWELL'S EQUATIONS IN CARNOT GROUPS

Communications in Contemporary Mathematics, 2012
In this paper we define Maxwell's equations in the setting of the intrinsic complex of differential forms in Carnot groups introduced by M. Rumin. It turns out that these equations are higher-order equations in the horizontal derivatives. In addition, when looking for a vector potential, we have to deal with a new class of higher-order evolution ...
FRANCHI, BRUNO, TESI, MARIA CARLA
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Normal families of mappings on Carnot groups

Siberian Mathematical Journal, 1996
A Carnot group is defined to be a connected simply connected nilpotent Lie group whose Lie algebra splits into the direct sum of vector spaces \(V_1\oplus \cdots \oplus V_r\) such that \([V_1,V_k] =V_{k+1}\) for \(1\leq k\leq r-1\) and \([V_1,V_r] =\{0\}\). The goal of the article is to consider normal classes of mappings on a Carnot group.
S. K. Vodop'yanov, N. A. Kudryavtseva
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Homogenization and Convergence of Correctors in Carnot Groups

Communications in Partial Differential Equations, 2005
ABSTRACT We consider homogenization of differential operators of the form where is a family of linearly independent vector fields in ℝ N that by commutation generate the Lie algebra of a Carnot group, a ij (ξ) are periodic functions in the sense of the group, and δ1/e are the dilations in the group. We establish Meyers type estimates for the horizontal
FRANCHI, BRUNO, Gutiérrez C. E., van Nguyen T.   +2 more
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Isoperimetric sets on Carnot groups

2003
The authors prove the existence of the isoperimetric set in Carnot groups, that is the existence of a set \(E\) minimizing the intrinsic perimeter \(P_G\) among all measurable sets of prescribed Lebesgue measure \(v\). The authors give also some regularity result of this set; they prove that the set \(E\) has a unique reduced equivalent set \(E_1 ...
LEONARDI, Gian Paolo, Rigot, Severine
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Cancer statistics for African American/Black People 2022

Ca-A Cancer Journal for Clinicians, 2022
Angela Giaquinto, Kimberly D Miller, Rebecca L Siegel   +2 more
exaly  

Cancer statistics for the US Hispanic/Latino population, 2021

Ca-A Cancer Journal for Clinicians, 2021
Kimberly D Miller, Paulo S Pinheiro, Priti Bandi   +2 more
exaly  

Cancer statistics for adolescents and young adults, 2020

Ca-A Cancer Journal for Clinicians, 2020
Kimberly D Miller, Heather S Hipp, Ahmedin Jemal Dvm   +2 more
exaly