2012/08/26 by Sagun Chanillo, Chanillo, Sagun, Hung-Lin Chiu +3 · 1 citation
Mathematics · #32V05 #32V20 #53C56 #Advanced Harmonic Analysis Research #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1208.5230
openalex publication_date 2012/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Ω be a bounded strictly pseudoconvex domain in C2 with a smooth, connected and compact boundary M and having a CR structure J0 induced from C2. Assume this CR structure has zero Webster torsion. Then if we deform the CR structure through real-analytic dependence on the deformation parameter and such that each deformed structure along the deformation path is smooth and embeddable in C2, we show that for small deformations of the CR structure J from J0, the associated CR Paneitz operator for J is non-negative. We also show that the Webster curvature for any ellipsoid in C2 is positive. The results in this paper complement and provide partial converses to our earlier paper, (to appear Duke Math. J.) arxiv: 1007.5020.