JournalsrmiVol. 39, No. 6pp. 2017–2066

On the Sobolev quotient of three-dimensional CR manifolds

  • Jih-Hsin Cheng

    Academia Sinica and NCTS 6F, Taipei, Taiwan (R.O.C.)

  • Andrea Malchiodi

    Scuola Normale Superiore, Pisa, Italy

  • Paul Yang

    Princeton University, USA
On the Sobolev quotient of three-dimensional CR manifolds cover
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Abstract

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.

Cite this article

Jih-Hsin Cheng, Andrea Malchiodi, Paul Yang, On the Sobolev quotient of three-dimensional CR manifolds. Rev. Mat. Iberoam. 39 (2023), no. 6, pp. 2017–2066

DOI 10.4171/RMI/1412