Calculus of Variations and Geometric Measure Theory

J. H. Cheng - A. Malchiodi - P. Yang

On the Sobolev quotient of three-dimensional CR manifolds

created by malchiodi on 09 Apr 2019


Submitted Paper

Inserted: 9 apr 2019
Last Updated: 9 apr 2019

Pages: 36
Year: 2019


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.