On the Sobolev quotient of three-dimensional CR manifolds
Differential Geometry
2019-04-10 v1 Analysis of PDEs
Abstract
We exhibit examples of compact three-dimensional CR manifolds of positive Webster class, {\em Rossi spheres}, for which the pseudo-hermitian mass as defined in \cite{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.
Keywords
Cite
@article{arxiv.1904.04665,
title = {On the Sobolev quotient of three-dimensional CR manifolds},
author = {Jih-Hsin Cheng and Andrea Malchiodi and Paul Yang},
journal= {arXiv preprint arXiv:1904.04665},
year = {2019}
}
Comments
36 pages, 2 figures