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Notions of Convexity in Carnot Groups [PDF]
Communications in Analysis and Geometry, 2003 The aim of this interesting paper is to study appropriate notions of convexity in the setting of Carnot groups \(G\). First, the notion of strong \(H\)-convexity is examined. Some arguments showing that the concept is to restrictive are presented. Then the notion of weakly \(H\)-convex functions is defined.
Duy Minh Nhieu +3 more
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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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Blowups and blowdowns of geodesics in Carnot groups
Journal of Differential Geometry, 2023 43 pages, 2 figures, included versions of the main theorems for weak tangents, revised section 5.2, to appear in the Journal of Differential ...
Hakavuori, Eero, Le Donne, Enrico
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Hilbert-Haar coordinates and Miranda's theorem in Lie groups
Bruno Pini Mathematical Analysis Seminar, 2020 We study the interior regularity of solutions to a class of quasilinear equations of non-degenerate p-Laplacian type on Lie groups that admit a system of Hilbert-Haar coordinates. These are coordinates with respect to which every linear function has zero
András Domokos, Juan J. Manfredi
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Nature and importance of follicular lymphoma precursors
Haematologica, 2014 It is now widely recognized that cancer development is a protracted process requiring the stepwise acquisition of multiple oncogenic events. In humans, this process can take decades, if not a lifetime, blurring the notion of ‘healthy’ individuals ...
Emilie Mamessier +6 more
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DFT screening of adsorption of biodiesel molecules on aluminum and stainless steel surfaces
Results in Surfaces and Interfaces, 2022 We present a Density Functional Theory (DFT) study of the adsorption of small organic molecules, taken as models of biodiesel autoxidation products, on stainless steel and aluminum surfaces.
Claudia Cantarelli +4 more
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Invertible Carnot Groups [PDF]
Analysis and Geometry in Metric Spaces, 2014 Abstract 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.
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On Viscosity and Equivalent Notions of Solutions for Anisotropic Geometric Equations
Abstract and Applied Analysis, 2020 We prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points.
Cecilia De Zan, Pierpaolo Soravia
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Conformal maps of Carnot groups
Annales Academiae Scientiarum Fennicae Mathematica, 2015 If f is a conformal mapping defined on a connected open subset of a Carnot group G, then either f is the composition of a translation, a dilation and an isometry, or G is the nilpotent Iwasawa component of a real rank 1 simple Lie group S, and f arises from the action of S on G, viewed as an open subset of S/P, where P is a parabolic subgroup of G and ...
Cowling, MG, Ottazzi, A
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Nonexistence Results for Semilinear Equations in Carnot Groups
Analysis and Geometry in Metric Spaces, 2013 In this paper, following [3], we provide some nonexistence results for semilinear equations in the the class of Carnot groups of type ★.This class, see [20], contains, in particular, all groups of step 2; like the Heisenberg group, and also Carnot ...
Ferrari Fausto, Pinamonti Andrea
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