Results 11 to 20 of about 109,220 (265)
Minimal surfaces in the Heisenberg group [PDF]
Geometriae Dedicata, 2006 We investigate the minimal surface problem in the three dimensional Heisenberg group, H, equipped with its standard Carnot-Caratheodory metric. Using a particular surface measure, we characterize minimal surfaces in terms of a sub-elliptic partial ...
Pauls, Scott D.
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Geodesics in the Heisenberg Group
Analysis and Geometry in Metric Spaces, 2015 We provide a new and elementary proof for the structure of geodesics in the Heisenberg group Hn. The proof is based on a new isoperimetric inequality for closed curves in R2n.We also prove that the Carnot- Carathéodory metric is real analytic away from ...
Hajłasz Piotr, Zimmerman Scott
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Fourier analysis on the Heisenberg group [PDF]
Proceedings of the National Academy of Sciences, 1977 We obtain a usable characterization of the (group) Fourier transform of 𝒮(H n ) (Schwartz space on the Heisenberg group). The characterization involves writing elements of [Formula: see text] as asymptotic series in Planck's constant.
Daryl Geller
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The Harmonic Oscillator on the Heisenberg Group [PDF]
Comptes Rendus. Mathématique, 2020 In this note we present a notion of harmonic oscillator on the Heisenberg group $\mathbf{H}_n$ which forms the natural analogue of the harmonic oscillator on $\mathbb{R}^n$ under a few reasonable assumptions: the harmonic oscillator on $\mathbf{H}_n ...
Rottensteiner, David, Ruzhansky, Michael
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CMC Spheres in the Heisenberg Group [PDF]
Analysis and Geometry in Metric Spaces, 2019 We study a family of spheres with constant mean curvature (CMC) in the Riemannian Heisenberg group H1. These spheres are conjectured to be the isoperimetric sets of H1. We prove several results supporting this conjecture.
Franceschi Valentina +2 more
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Group projector generalization of dirac-heisenberg model [PDF]
, 2000 The general form of the operators commuting with the ground representation (appearing in many physical problems within single particle approximation) of the group is found.
Altmann S L +9 more
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Riesz Potential on the Heisenberg Group [PDF]
Journal of Inequalities and Applications, 2011 The relation between Riesz potential and heat kernel on the Heisenberg group is studied. Moreover, the Hardy-Littlewood-Sobolev inequality is established.
Jianxun He, Jinsen Xiao
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The braided Heisenberg group [PDF]
Journal of Mathematical Physics, 1993 The braided groups and braided matrices B(R) for the solution R of the Yang–Baxter equation associated to the quantum Heisenberg group are computed. It is also shown that a particular extension of the quantum Heisenberg group is dual to the Heisenberg universal enveloping algebra Uq(h), and this result is used to derive an action of Uq(h) on the ...
Shahn Majid, W. K. Baskerville
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Deformation quantization of the Heisenberg group [PDF]
Communications in Mathematical Physics, 1994 (TeX 9 pages, some misprints are here corrected)
BONECHI F. +3 more
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Dorronsoro's theorem in Heisenberg groups [PDF]
Bulletin of the London Mathematical Society, 2020 A theorem of Dorronsoro from the 1980s quantifies the fact that real-valued Sobolev functions on Euclidean spaces can be approximated by affine functions almost everywhere, and at all sufficiently small scales. We prove a variant of Dorronsoro's theorem in Heisenberg groups: functions in horizontal Sobolev spaces can be approximated by affine functions
Orponen, Tuomas, Fässler, Katrin
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