Results 21 to 30 of about 18,179 (207)
Blowups and blowdowns of geodesics in Carnot groups
Journal of Differential Geometry, 2023 43 pages, 2 figures, included versions of the main theorems for weak tangents, revised section 5.2, to appear in the Journal of Differential ...
Hakavuori, Eero, Le Donne, Enrico
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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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Structure of porous sets in Carnot groups [PDF]
Illinois Journal of Mathematics, 2017 23 ...
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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Multicomplexes on Carnot Groups and Their Associated Spectral Sequence. [PDF]
J Geom Anal, 2023 AbstractThe aim of this paper is to give a thorough insight into the relationship between the Rumin complex on Carnot groups and the spectral sequence obtained from the filtration on forms by homogeneous weights that computes the de Rham cohomology of the underlying group.
Lerario A, Tripaldi F.
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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.
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Exceptional families of measures on Carnot groups
Analysis and Geometry in Metric Spaces, 2023 AbstractWe study the families of measures on Carnot groups that have vanishingpp-module, which we callMp{M}_{p}-exceptional families. We found necessary and sufficient Conditions for the family of intrinsic Lipschitz surfaces passing through a common point to beMp{M}_{p}-exceptional forp≥1p\ge 1.
Franchi, Bruno, Markina, Irina
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Conformal and CR mappings on Carnot groups [PDF]
Proceedings of the American Mathematical Society, Series B, 2020 We consider a class of stratified groups with a CR structure and a compatible control distance. For these Lie groups we show that the space of conformal maps coincide with the space of CR and anti-CR diffeomorphisms. Furthermore, we prove that on products of such groups, all CR and anti-CR maps are product maps, up to a permutation isomorphism, and ...
Cowling, MG, Li, J, Ottazzi, A, Wu, Q
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Heat and entropy flows in Carnot groups [PDF]
Revista Matemática Iberoamericana, 2019 We prove the correspondence between the solutions of the sub-elliptic heat equation in a Carnot group \mathbb G and the gradient flows of the relative entropy functional in the Wasserstein space of probability measures on \mathbb G ...
Ambrosio L., Stefani G.
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Subelliptic and parametric equations on Carnot groups [PDF]
Proceedings of the American Mathematical Society, 2015 This article concerns a class of elliptic equations on Carnot groups depending on one real parameter. Our approach is based on variational methods. More precisely, we establish the existence of at least two weak solutions for the treated problem by using a direct consequence of the celebrated Pucci-Serrin theorem and of a local minimum result for ...
Molica Bisci G, Ferrara M
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