On the Sobolev quotient of three-dimensional CR manifolds

Jih Hsin Cheng, Andrea Malchiodi, Paul Yang

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)2017-2066
Number of pages50
JournalRevista Matematica Iberoamericana
Issue number6
StatePublished - 2023

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • CR manifold
  • CR-Sobolev quotient
  • pseudo-hermitian mass
  • Rossi sphere


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