1,721,090 research outputs found
On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups
No full textWe show by explicit estimates that the SubRiemannian distance in a Carnot group of step two is locally semiconcave away from the diagonal if and only if the group does not contain abnormal minimizing curves. Moreover, we prove that local semiconcavity fails to hold in the step-3 Engel group, even in the weaker “horizontal” sense
Nonsmooth solutions for a class of fully nonlinear PDE's on Lie groups
No full textIn this paper we prove the existence of nonsmooth viscosity solutions for Dirichlet problems involving a class a fully non-linear operators on Lie groups. In particular we consider the elementary symmetric functions of the eigenvalues of the Hessian built with left-invariant vector fields
Maximum and comparison principles for convex functions on the Heisenberg group
No full textWe prove estimates, similar in form to the classical Aleksandrov estimates, for a Monge-Ampere type operator on the Heisenberg group. A notion of normal mapping does not seem to be available in this context and the method of our proof uses integration by parts. We first identify the null Lagrangian in the Heisenberg group and prove mononicity properties of Hessian integrals and oscillation estimates that lead to the construction of an analogue of Monge-Ampere measures for convex functions in the Heisenberg group
Nonsmooth viscosity solutions of elementary symmetric functions of the complex Hessian
No full textIn this paper we prove the existence of nonsmooth viscosity solutions for Dirichlet problems involving elementary symmetric functions of the eigenvalues of the complex Hessian
Abstract approach to non homogeneous Harnack inequality in doubling quasi metric spaces
No full textWe develop an abstract theory to obtain Harnack inequality for non homogeneous PDEs in the setting of quasi metric spaces. The main idea is to adapt the notion of double ball and critical density property given by Di Fazio, Gutierrez, Lanconelli, taking into account the right hand side of the equation. Then we apply the abstract procedure to the case of subelliptic equations in non divergence form involving Grushin vector fields and to the case of X-elliptic operators in divergence form
Sub-Riemannian cut time and cut locus in Reiter–Heisenberg groups
Full text linkWe study the sub-Riemannian cut time and cut locus of a given point in a class of step-2 Carnot groups of Reiter–Heisenberg type. Following the Hamiltonian point of view, we write and analyze extremal curves, getting the cut time of any of them, and a precise description of the set of cut points
On the subRiemannian cut locus in a model of free two-step Carnot group
Full text linkWe 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). We also calculate explicitly the cut time of any extremal path and the distance from the origin of all points of the cut locus. Furthermore, by using the Hamiltonian approach, we show that the cut time of strictly normal extremal paths is a smooth explicit function of the initial velocity covector. Finally, using our previous results, we show that at any cut point the distance has a corner-like singularity
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
A HADAMARD-TYPE OPEN MAP THEOREM FOR SUBMERSIONS AND APPLICATIONS TO COMPLETENESS RESULTS IN CONTROL THEORY
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