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arXiv · 1904.04665

On the Sobolev quotient of three-dimensional CR manifolds

Jih-Hsin Cheng·Andrea Malchiodi·Paul Yang
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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.

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Jih-Hsin Cheng, Andrea Malchiodi, Paul Yang. 2019-04-09. On the Sobolev quotient of three-dimensional CR manifolds. https://arxiv.org/abs/1904.04665

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