Beltrami Equations on Rossi Spheres

Elisabetta Barletta, Sorin Dragomir and Francesco Esposito
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Elisabetta Barletta: Dipartimento di Matematica, Informatica ed Economia, Universita` degli Studi della Basilicata, 85100 Potenza, Italy
Sorin Dragomir: Dipartimento di Matematica, Informatica ed Economia, Universita` degli Studi della Basilicata, 85100 Potenza, Italy
Francesco Esposito: Dipartimento di Matematica, Informatica ed Economia, Universita` degli Studi della Basilicata, 85100 Potenza, Italy

Mathematics, 2022, vol. 10, issue 3, 1-40

Abstract: Beltrami equations L ¯ t ( g ) = μ ( · , t ) L t ( g ) on S 3 (where L t , | t | < 1 , are the Rossi operators i.e., L t spans the globally nonembeddable CR structure H ( t ) on S 3 discovered by H. Rossi) are derived such that to describe quasiconformal mappings f : S 3 → N ⊂ C 2 from the Rossi sphere S 3 , 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 g t such that g t − v ∈ W F 1 , 2 S 3 , θ with v ∈ CR ∞ S 3 , H ( 0 ) .

Keywords: CR manifold; Tanaka–Webster connection; Fefferman metric; Lewy operator; Heisenberg group; quasiconformal map; Beltrami equation; Rossi sphere; Bargmann representation; Fourier transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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