Results 31 to 40 of about 18,321 (180)
A note on Carnot geodesics in nilpotent Lie groups [PDF]
, 1995 We show that strictly abnormal geodesics arise in graded nilpotent Lie groups. We construct such a group, for which some Carnot geodesics are strictly abnormal; in fact, they are not normal in any subgroup.
Golé, Christopher, Karidi, Ron
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Porosity, Differentiability and Pansu's Theorem
, 2016 We use porosity to study differentiability of Lipschitz maps on Carnot groups. Our first result states that directional derivatives of a Lipschitz function act linearly outside a $\sigma$-porous set.
Pinamonti, Andrea, Speight, Gareth
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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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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 ...
Flynn Joshua, Lam Nguyen, Lu Guozhen
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Geometric inequalities in Carnot groups [PDF]
, 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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X-states from a finite geometric perspective
Results in Physics, 2021 It is found that 15 different types of two-qubit X-states split naturally into two sets (of cardinality 9 and 6) once their entanglement properties are taken into account.
Colm Kelleher +3 more
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Isodiametric inequality in Carnot groups
, 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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On the Lie Algebra of polarizable Carnot groups [PDF]
Analysis and Mathematical Physics, 2020 Let \(G\) be a Carnot group equipped with a left-invariant sub-Riemannian metric, induced by an inner product \(\langle \cdot, \cdot \rangle\) on the first layer of its Lie algebra \(\mathfrak{g}\). The metric induces a family of \(p\)-sub-Laplacians \(\Delta_p\) on \(G\), where \(\Delta_2\) is the usual sub-Laplacian. Following [\textit{Z. M.
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Subelliptic and parametric equations on Carnot groups [PDF]
Proceedings of the American Mathematical Society, 2015 This article concerns a class of elliptic equations on Carnot groups depending on one real parameter. Our approach is based on variational methods. More precisely, we establish the existence of at least two weak solutions for the treated problem by using a direct consequence of the celebrated Pucci-Serrin theorem and of a local minimum result for ...
Molica Bisci G, Ferrara M
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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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