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Keywords = Rossi sphere

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40 pages, 463 KB  
Article
Beltrami Equations on Rossi Spheres
by Elisabetta Barletta, Sorin Dragomir and Francesco Esposito
Mathematics 2022, 10(3), 371; https://doi.org/10.3390/math10030371 - 25 Jan 2022
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Abstract
Beltrami equations L¯t(g)=μ(·,t)Lt(g) on S3 (where Lt, |t|<1, are the Rossi operators i.e., Lt spans the globally [...] Read more.
Beltrami equations L¯t(g)=μ(·,t)Lt(g) on S3 (where Lt, |t|<1, are the Rossi operators i.e., Lt spans the globally nonembeddable CR structure H(t) on S3 discovered by H. Rossi) are derived such that to describe quasiconformal mappings f:S3NC2 from the Rossi sphere S3,H(t). Using the Greiner–Kohn–Stein solution to the Lewy equation and the Bargmann representations of the Heisenberg group, we solve the Beltrami equations for Sobolev-type solutions gt such that gtvWF1,2S3,θ with vCRS3,H(0). Full article
(This article belongs to the Special Issue Differential Geometry: Theory and Applications Part II)
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