Results 1 to 10 of about 12,518,220 (217)
On the H.-Q. Li inequality on step-two Carnot groups [PDF]
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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A Cornucopia of Carnot Groups in Low Dimensions [PDF]
Analysis and Geometry in Metric Spaces, 2022 Stratified groups are those simply connected Lie groups whose Lie algebras admit a derivation for which the eigenspace with eigenvalue 1 is Lie generating.
Le Donne Enrico, Tripaldi Francesca
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Direct Assembly of Micrometer-Long Polymeric Cylinders in Water via Supramolecular Sticker Engineering. [PDF]
Macromol Rapid CommunEngineering order at the nanoscale: Tailored design of PDI and TEG‐functionalized poly(N,N‐dimethylacrylamide) enables direct assembly of micrometer‐long nanocylinders in water. TEG prevents clustering, while the polymer chain length governs the morphology.
Berruée S +6 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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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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Hilbert-Haar coordinates and Miranda's theorem in Lie groups
Bruno Pini Mathematical Analysis Seminar, 2020 We study the interior regularity of solutions to a class of quasilinear equations of non-degenerate p-Laplacian type on Lie groups that admit a system of Hilbert-Haar coordinates. These are coordinates with respect to which every linear function has zero
András Domokos, Juan J. Manfredi
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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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Analysis and Geometry in Metric Spaces, 2014 We characterize Carnot groups admitting a 1-quasiconformal metric inversion as the Lie groups of Heisenberg type whose Lie algebras satisfy the J2-condition, thus characterizing a special case of inversion invariant bi-Lipschitz homogeneity.
Freeman David M.
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Analysis and Geometry in Metric Spaces, 2018 Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance.
Le Donne Enrico
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