On the Sobolev quotient of three-dimensional CR manifolds

Jih Hsin Cheng; Andrea Malchiodi; Paul Yang

doi:10.4171/RMI/1412

On the Sobolev quotient of three-dimensional CR manifolds

Jih Hsin Cheng, Andrea Malchiodi, Paul Yang

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2017-2066
Number of pages	50
Journal	Revista Matematica Iberoamericana
Volume	39
Issue number	6
DOIs	https://doi.org/10.4171/RMI/1412
State	Published - 2023

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

CR manifold
CR-Sobolev quotient
Rossi sphere
pseudo-hermitian mass

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10.4171/RMI/1412

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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.",

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AU - Malchiodi, Andrea

AU - Yang, Paul

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AB - 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.

KW - CR manifold

KW - CR-Sobolev quotient

KW - Rossi sphere

KW - pseudo-hermitian mass

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JO - Revista Matematica Iberoamericana

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On the Sobolev quotient of three-dimensional CR manifolds

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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