Results 11 to 20 of about 14,114 (194)
Analysis and Geometry in Metric Spaces, 2014 We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity.
Freeman David M.
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Intrinsic Lipschitz Graphs Within Carnot Groups [PDF]
The Journal of Geometric Analysis, 2015 Carnot groups are connected, simply connected, nilpotent Lie groups whose Lie algebra admits a stratification. Hence, the easiest nontrivial class of examples of Carnot groups are Heisenberg groups. In this well-written paper, the authors examine a general notion of intrinsic submanifolds in Carnot groups, called \textit{Intrinsic Lipschitz graphs ...
FRANCHI, BRUNO, Serapioni, Raul Paolo
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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
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Ricci curvatures in Carnot groups
Mathematical Control & Related Fields, 2013 29 pages, 1 ...
Ludovic Rifford
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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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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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Yamabe-type equations on Carnot groups
Potential Analysis, 2016 This article is concerned with a class of elliptic equations on Carnot groups depending of one real positive parameter and involving a critical nonlinearity.
Bisci, Giovanni Molica +1 more
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Uniqueness and comparison principles for semilinear equations and inequalities in Carnot groups
Advances in Nonlinear Analysis, 2018 Variants of the Kato inequality are proved for distributional solutions of semilinear equations and inequalities on Carnot groups. Various applications to uniqueness, comparison of solutions and Liouville theorems are presented.
D’Ambrosio Lorenzo, Mitidieri Enzo
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On rectifiable measures in Carnot groups: representation. [PDF]
Calc Var Partial Differ Equ, 2022 AbstractThis paper deals with the theory of rectifiability in arbitrary Carnot groups, and in particular with the study of the notion of $$\mathscr {P}$$ P -rectifiable measure. First, we show that in arbitrary Carnot groups the natural infinitesimal definition of rectifiabile measure, i.e., the definition given in ...
Antonelli G, Merlo A.
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Rearrangements in Carnot Groups [PDF]
Acta Mathematica Sinica, English Series, 2019 In this paper we extend the notion of rearrangement of nonnegative functions to the setting of Carnot groups. We define rearrangement with respect to a given family of anisotropic balls B_r or equivalently with respect to a gauge |x|, and prove basic regularity properties of this construction.
Manfredi, Juan J. +1 more
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