Mathematics > Differential Geometry
arXiv:2606.24508 (math)
[Submitted on 23 Jun 2026]
Abstract:The CR Paneitz operator is closely related to several important problems in CR geometry. In this paper, we study the CR Paneitz operator on non-embeddable three-dimensional tori. Under mild assumptions, we show that it possesses infinitely many negative eigenvalues. We also provide concrete examples satisfying the assumptions.
| Comments: | 24 pages |
| Subjects: | Differential Geometry (math.DG); Analysis of PDEs (math.AP); Complex Variables (math.CV); Spectral Theory (math.SP) |
| MSC classes: | 32V10, 32V20, 32V30, 35P15, 58J50 |
| Cite as: | arXiv:2606.24508 [math.DG] |
| (or arXiv:2606.24508v1 [math.DG] for this version) | |
| https://doi.org/10.48550/arXiv.2606.24508 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Yuya Takeuchi [view email]
[v1]
Tue, 23 Jun 2026 12:40:44 UTC (69 KB)
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