Results 61 to 70 of about 18,321 (180)
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. As a special case of our results we prove the existence of at least one nontrivial solution for a subelliptic critical equation defined on a smooth and bounded domain $D$ of the {Heisenberg group}
Molica Bisci G, Repovs D
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Analysis and Geometry in Metric SpacesIn the realm of sub-Riemannian manifolds, a relevant question is: what are the metric lines (isometric embedding of the real line)? The space of kk-jets of a real function of one real variable xx, denoted by Jk(R,R){J}^{k}\left({\mathbb{R}},{\mathbb{R}}),
Bravo-Doddoli Alejandro
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Abstract and Applied Analysis, 2014 Let {X1,X2,…,Xm} be the basis of space of horizontal vector fields in a Carnot group G=(Rn ...
Pengcheng Niu, Kelei Zhang
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A sufficient condition for nonrigidity of Carnot groups [PDF]
, 2018 In this article we consider contact mappings on Carnot groups. Namely, we are interested in those mappings whose differential preserves the horizontal space, defined by the first stratum of the natural stratification of the Lie algebra of a Carnot group.
Ottazzi, Alessandro
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A Decade with VAMDC: Results and Ambitions
Atoms, 2020 This paper presents an overview of the current status of the Virtual Atomic and Molecular Data Centre (VAMDC) e-infrastructure, including the current status of the VAMDC-connected (or to be connected) databases, updates on the latest technological ...
Damien Albert +72 more
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c horizontal convexity on Carnot groups
, 2010 Given a real-valued function $c$ defined on the cartesian product of a generic Carnot group $\G$ and the first layer $V_1$ of its Lie algebra, we introduce a notion of $c$ horizontal convex ($c$ H-convex) function on $\G$ as the supremum of a suitable family of affine functions; this family is defined pointwisely, and depends strictly on the horizontal
CALOGERO, ANDREA GIOVANNI, PINI, RITA
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Some Results on Maps That Factor through a Tree
Analysis and Geometry in Metric Spaces, 2015 We give a necessary and sufficient condition for a map deffned on a simply-connected quasi-convex metric space to factor through a tree. In case the target is the Euclidean plane and the map is Hölder continuous with exponent bigger than 1/2, such maps ...
Züst Roger
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Exceptional sets for self-similar fractals in Carnot groups [PDF]
, 2017 We consider self-similar iterated function systems in the sub-Riemannian setting of Carnot groups. We estimate the Hausdorff dimension of the exceptional set of translation parameters for which the Hausdorff dimension in terms of the Carnot-Carathéodory ...
BALOGH, ZOLTÁN M. +3 more
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Lipschitz and bilipschitz maps on Carnot groups [PDF]
Pacific Journal of Mathematics, 2013 Suppose A is an open subset of a Carnot group G, where G has a discrete analogue, and H is another Carnot group. We show that a Lipschitz function from A to H whose image has positive Hausdorff measure in the appropriate dimension is biLipschitz on a subset of A of positive Hausdorff measure.
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NanophotonicsWe look back at many challenges as well as unexpected successes encountered by the Mamyshev optical regenerator, which combines spectral broadening from self-phase modulation followed by offset bandpass filtering.
Finot Christophe, Rochette Martin
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