On the Sobolev quotient of three-dimensional CR manifolds

• Jih-Hsin Cheng ^[2] ; Andrea Malchiodi ^[3] ; Paul Yang ^[1]
  1. [1] Princeton University

     Princeton University

     Estados Unidos

     
  2. [2] Academia Sinica and NCTS 6F, Taipei, Taiwan
  3. [3] Scuola Normale Superiore, Pisa, Italy

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 39, Nº 6, 2023, págs. 2017-2066
• Idioma: inglés
• DOI: 10.4171/RMI/1412
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• Resumen

  • We exhibit examples of compact three-dimensional CR manifolds of positive Webster class, Rossi spheres, for which the pseudo-hermitian mass, as defined by Cheng–Malchiodi–Yang (2017), is negative, and for which the infimum of the CR-Sobolev quotient is not attained. To our knowledge, this is the first geometric context on smooth closed manifolds where this phenomenon arises, in striking contrast to the Riemannian case