CR Paneitz operator on non-embeddable CR manifolds
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909492656996352 |
|---|---|
| author | Takeuchi, Yuya |
| author_facet | Takeuchi, Yuya |
| contents | The CR Paneitz operator is closely related to some important problems in CR geometry. In this paper, we consider this operator on a non-embeddable CR manifold. This operator is essentially self-adjoint and its spectrum is discrete except zero. Moreover, the eigenspace corresponding to each non-zero eigenvalue is a finite dimensional subspace of the space of smooth functions. Furthermore, we show that the CR Paneitz operator on the Rossi sphere, an example of non-embeddable CR manifolds, has infinitely many negative eigenvalues, which is significantly different from the embeddable case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16185 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | CR Paneitz operator on non-embeddable CR manifolds Takeuchi, Yuya Complex Variables Analysis of PDEs Differential Geometry Spectral Theory 32V20, 58J50 The CR Paneitz operator is closely related to some important problems in CR geometry. In this paper, we consider this operator on a non-embeddable CR manifold. This operator is essentially self-adjoint and its spectrum is discrete except zero. Moreover, the eigenspace corresponding to each non-zero eigenvalue is a finite dimensional subspace of the space of smooth functions. Furthermore, we show that the CR Paneitz operator on the Rossi sphere, an example of non-embeddable CR manifolds, has infinitely many negative eigenvalues, which is significantly different from the embeddable case. |
| title | CR Paneitz operator on non-embeddable CR manifolds |
| topic | Complex Variables Analysis of PDEs Differential Geometry Spectral Theory 32V20, 58J50 |
| url | https://arxiv.org/abs/2407.16185 |