Results 11 to 20 of about 964 (155)
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
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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
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Rectifiability in Carnot Groups [PDF]
, 2022 This thesis is devoted to the study of the theory of rectifiability of sets and measures in the non smooth context of Carnot groups. The focus is on the study of the notion of P-rectifiability and its relation with other notions of rectifiability in Carnot groups.
ANTONELLI, GIOACCHINO
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Conformality and Q-harmonicity in Carnot groups
Duke Mathematical Journal, 2006 The main theorem of this paper is that 1-quasiconformal maps are smooth in all Carnot groups. This theorem can be used to prove rigidity theorems for quasiconformal maps between open subsets in certain classes of groups without any a priori smoothness assumption.
Capogna, Luca, Cowling, Michael
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Infinite-Dimensional Carnot Groups and Gâteaux Differentiability [PDF]
The Journal of Geometric Analysis, 2019 The article under review contributes to research based around Rademacher's theorem, which states that a Lipschitz mapping between two Euclidean spaces is differentiable almost everywhere with respect to the Lebesgue measure. More specifically, the article joins a flourishing branch of research which has the broad aim of extending Rademacher's theorem ...
Le Donne E., Li S., Moisala T.
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Cordes nonlinear operators in Carnot groups
Electronic Journal of Differential Equations, 2015 Our aim is to obtain L^p estimates for the second-order horizontal derivatives of the solutions for a nondivergence form nonlinear equation in Carnot groups.
Giuseppe Di Fazio +1 more
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A metric characterization of Carnot groups [PDF]
Proceedings of the American Mathematical Society, 2014 We give a short axiomatic introduction to Carnot groups and their subRiemannian and subFinsler geometry. We explain how such spaces can be metrically described as exactly those proper geodesic spaces that admit dilations and are isometrically homogeneous.
Le Donne, Enrico
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On the H.-Q. Li inequality on step-two Carnot groups
Comptes Rendus. Mathématique, 2023 In this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. We also establish the Riemannian counterpart of the H.-Q.
Zhang, Ye
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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
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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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