Results 21 to 30 of about 5,405,878 (192)
Rearrangements in Carnot Groups [PDF]
Acta Mathematica Sinica, English Series, 2019 In this paper we extend the notion of rearrangement of nonnegative functions to the setting of Carnot groups. We define rearrangement with respect to a given family of anisotropic balls B_r or equivalently with respect to a gauge |x|, and prove basic regularity properties of this construction.
Manfredi, Juan J. +1 more
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Notions of Convexity in Carnot Groups [PDF]
Communications in Analysis and Geometry, 2003 The aim of this interesting paper is to study appropriate notions of convexity in the setting of Carnot groups \(G\). First, the notion of strong \(H\)-convexity is examined. Some arguments showing that the concept is to restrictive are presented. Then the notion of weakly \(H\)-convex functions is defined.
DANIELLI D. +2 more
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Identifying 1-rectifiable measures in Carnot groups
Analysis and Geometry in Metric Spaces, 2023 We continue to develop a program in geometric measure theory that seeks to identify how measures in a space interact with canonical families of sets in the space. In particular, extending a theorem of M. Badger and R.
Badger Matthew, Li Sean, Zimmerman Scott
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Exceptional families of measures on Carnot groups
Analysis and Geometry in Metric Spaces, 2023 We study the families of measures on Carnot groups that have vanishing pp-module, which we call Mp{M}_{p}-exceptional families. We found necessary and sufficient Conditions for the family of intrinsic Lipschitz surfaces passing through a common point to ...
Franchi Bruno, Markina Irina
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Structure of porous sets in Carnot groups [PDF]
Illinois Journal of Mathematics, 2017 We show that any Carnot group contains a closed nowhere dense set which has measure zero but is not $σ$-porous with respect to the Carnot-Carathéodory (CC) distance. In the first Heisenberg group we observe that there exist sets which are porous with respect to the CC distance but not the Euclidean distance and vice-versa.
Pinamonti A., Speight G.
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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
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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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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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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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On Viscosity and Equivalent Notions of Solutions for Anisotropic Geometric Equations
Abstract and Applied Analysis, 2020 We prove that viscosity solutions of geometric equations in step two Carnot groups can be equivalently reformulated by restricting the set of test functions at the singular points.
Cecilia De Zan, Pierpaolo Soravia
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