CR Paneitz operator on non-embeddable CR manifolds
Complex Variables
2025-02-17 v2 Analysis of PDEs
Differential Geometry
Spectral Theory
Abstract
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.
Cite
@article{arxiv.2407.16185,
title = {CR Paneitz operator on non-embeddable CR manifolds},
author = {Yuya Takeuchi},
journal= {arXiv preprint arXiv:2407.16185},
year = {2025}
}
Comments
15 page, I modified the proof of the main theorem and added new results on the spectral projection