Results 21 to 30 of about 12,576,498 (281)
Stochastic homogenization for functionals with anisotropic rescaling and non-coercive Hamilton-Jacobi equations [PDF]
, 2017 We study the stochastic homogenization for a Cauchy problem for a first-order Hamilton-Jacobi equation whose operator is not coercive w.r.t. the gradient variable.
Dirr, Nicolas +3 more
core +4 more sources
A notion of rectifiability modeled on Carnot groups [PDF]
, 2004 We introduce a notion of rectifiability modeled on Carnot groups. Precisely, we say that a subset E of a Carnot group M and N is a subgroup of M, we say E is N-rectifiable if it is the Lipschitz image of a positive measure subset of N.
Pauls, Scott D.
core +4 more sources
The Traveling Salesman Theorem in Carnot groups [PDF]
Calculus of Variations and Partial Differential Equations, 2018 Let $\mathbb{G}$ be any Carnot group. We prove that, if a subset of $\mathbb{G}$ is contained in a rectifiable curve, then it satisfies Peter Jones' geometric lemma with some natural modifications. We thus prove one direction of the Traveling Salesman Theorem in $\mathbb{G}$.
Chousionis, Vasilis +2 more
openaire +3 more sources
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
doaj +1 more source
Quasisymmetric maps of boundaries of amenable hyperbolic groups [PDF]
, 2014 In this paper we show that if $Y=N \times \mathbb{Q}_m$ is a metric space where $N$ is a Carnot group endowed with the Carnot-Caratheodory metric then any quasisymmetric map of $Y$ is actually bilipschitz. The key observation is that $Y$ is the parabolic
Dymarz, Tullia
core +1 more source
Convex functions on Carnot groups
Revista Matemática Iberoamericana, 2007 We consider the definition and regularity properties of convex functions in Carnot groups. We show that various notions of convexity in the subelliptic setting that have appeared in the literature are equivalent. Our point of view is based on thinking of convex functions as subsolutions of homogeneous elliptic equations.
P. JUUTINEN +3 more
openaire +6 more sources
Rigidity of 2-Step Carnot Groups [PDF]
The Journal of Geometric Analysis, 2017 Except for minor polishing this version is enriched with two appendices concerning pseudo H-type algebras with J^2-condition. In Appendix A we relate these algebras to division algebras and their split versions.
Mauricio Godoy Molina +3 more
openaire +3 more sources
Laser-induced thermoelectric effects in electrically biased nanoscale constrictions
Nanophotonics, 2018 Electrically biased metal nanostructures are at the core of innovative multifunctional integrated devices that control the flow of electrons and photons at the nanoscale.
Mennemanteuil Marie-Maxime +6 more
doaj +1 more source
Monge's transport problem in the Heisenberg group [PDF]
, 2010 We prove the existence of solutions to Monge transport problem between two compactly supported Borel probability measures in the Heisenberg group equipped with its Carnot-Caratheodory distance assuming that the initial measure is absolutely continuous ...
Ambrosio B. +15 more
core +6 more sources