Heisenberg quasiregular ellipticity

• Katrin Fässler ^[1] ; Anton Lukyanenko ^[2] ; Jeremy Tyson ^[3]
  1. [1] University of Jyväskylä

     University of Jyväskylä

     Jyväskylä, Finlandia

     
  2. [2] George Mason University

     George Mason University

     Estados Unidos

     
  3. [3] University of Illinois

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 2, 2019, págs. 471-520
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • Following the Euclidean results of Varopoulos and Pankka–Rajala, we provide a necessary topological condition for a sub-Riemannian 3-manifold M to admit a nonconstant quasiregular mapping from the sub-Riemannian Heisenberg group H. As an application, we show that a link complement S3∖L has a sub-Riemannian metric admitting such a mapping only if L is empty, an unknot or Hopf link. In the converse direction, if L is empty, a specific unknot or Hopf link, we construct a quasiregular mapping from H to S3∖L.