J. H. Cheng - A. Malchiodi - P. Yang
On the Sobolev quotient of three-dimensional CR manifolds
Submitted Paper
Inserted: 9 apr 2019
Last Updated: 9 apr 2019
Pages: 36
Year: 2019
Abstract:
We exhibit examples of compact three-dimensional CR manifolds of positive Webster class, Rossi spheres, for which the pseudo-hermitian mass as defined in CMY17 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.
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