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Beltrami Equations on Rossi Spheres

Author

Listed:
  • Elisabetta Barletta

    (Dipartimento di Matematica, Informatica ed Economia, Universita` degli Studi della Basilicata, 85100 Potenza, Italy
    These authors contributed equally to this work.)

  • Sorin Dragomir

    (Dipartimento di Matematica, Informatica ed Economia, Universita` degli Studi della Basilicata, 85100 Potenza, Italy
    These authors contributed equally to this work.)

  • Francesco Esposito

    (Dipartimento di Matematica, Informatica ed Economia, Universita` degli Studi della Basilicata, 85100 Potenza, Italy
    These authors contributed equally to this work.)

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 ) .

Suggested Citation

  • Elisabetta Barletta & Sorin Dragomir & Francesco Esposito, 2022. "Beltrami Equations on Rossi Spheres," Mathematics, MDPI, vol. 10(3), pages 1-40, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:371-:d:734031
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