Results 31 to 40 of about 12,258,354 (255)
A note on monotonicity and Bochner formulas in Carnot groups [PDF]
Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2022 In this note, we prove two monotonicity formulas for solutions of $\Delta _H f = c$ and $\Delta _H f - \partial _t f = c$ in Carnot groups. Such formulas involve the right-invariant carré du champ of a function and they are false for the left-invariant ...
N. Garofalo
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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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Some counterexamples to Alt–Caffarelli–Friedman monotonicity formulas in Carnot groups [PDF]
Annali di Matematica Pura ed ApplicataIn this paper we continue the analysis of an Alt–Caffarelli–Friedman (ACF) monotonicity formula in Carnot groups of step $$s >1$$ s > 1 confirming the existence of counterexamples to the monotone increasing behavior.
Fausto Ferrari, Davide Giovagnoli
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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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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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Conformal maps of Carnot groups
Annales Academiae Scientiarum Fennicae Mathematica, 2015 If f is a conformal mapping defined on a connected open subset of a Carnot group G, then either f is the composition of a translation, a dilation and an isometry, or G is the nilpotent Iwasawa component of a real rank 1 simple Lie group S, and f arises from the action of S on G, viewed as an open subset of S/P, where P is a parabolic subgroup of G and ...
Cowling, MG, Ottazzi, A
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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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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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Horizontal semiconcavity for the square of Carnot–Carathéodory distance on step 2 Carnot groups and applications to Hamilton–Jacobi equations [PDF]
NonlinearityWe show that the square of Carnot–Carathéodory distance from the origin, in step 2 Carnot groups, enjoys the horizontal semiconcavity (h-semiconcavity) everywhere in the group including the origin. We first give a proof in the case of ideal Carnot groups,
Federica Dragoni, Qing Liu, Ye Zhang
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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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