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On the subRiemannian cut locus in a model of free two-step Carnot group
Calculus of Variations and Partial Differential Equations, 2016We characterize the subRiemannian cut locus of the origin in the free Carnot group of step two with three generators, giving a new, independent proof of a result by Myasnichenko (J Dyn Control Syst 8(4):573-597, 2002).
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Intrinsic diophantine approximation in Carnot groups and in the Siegel model of the Heisenberg group
Monatshefte für Mathematik (Print), 2020We study an intrinsic notion of Diophantine approximation on a rational Carnot group G . If G has Hausdorff dimension Q , we show that its Diophantine exponent is equal to $$(Q+1)/Q$$ ( Q + 1 ) / Q , generalizing the case $$G=\mathbb {R}^n$$ G = R n . We
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In this paper, we will obtain the new results of the strong and weak Spanne-Guliyev, Adams-Guliyev and Adams-Gunawan type boundedness characterization of the fractional maximal operator in generalized Morrey spaces, respectively. Moreover, we will give a
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