On the Sobolev quotient of three-dimensional CR manifolds

2019/04/09 by Jih-Hsin Cheng, Cheng, Jih-Hsin, Andrea Malchiodi +3 · 1 citation
Mathematics · #32V20 #32V30 #35J20 #35J75 #53C17 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1904.04665

openalex publication_date 2019/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeCMY17 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.

Citations

• On the proof of the positive mass conjecture in general relativity

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• The GJMS operators in geometry, analysis, and physics

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