Analysis of the critical CR GJMS operator
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866910538160668672 |
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| author | Takeuchi, Yuya |
| author_facet | Takeuchi, Yuya |
| contents | The critical CR GJMS operator on a strictly pseudoconvex CR manifold is a non-hypoelliptic CR invariant differential operator. We prove that, under the embeddability assumption, it is essentially self-adjoint and has closed range. Moreover, its spectrum is discrete, and the eigenspace corresponding to each non-zero eigenvalue is a finite-dimensional subspace of the space of smooth functions. As an application, we obtain a necessary and sufficient condition for the existence of a contact form with zero CR $Q$-curvature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_13813 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Analysis of the critical CR GJMS operator Takeuchi, Yuya Differential Geometry Analysis of PDEs Complex Variables Spectral Theory 32V20, 35P05, 58J40 The critical CR GJMS operator on a strictly pseudoconvex CR manifold is a non-hypoelliptic CR invariant differential operator. We prove that, under the embeddability assumption, it is essentially self-adjoint and has closed range. Moreover, its spectrum is discrete, and the eigenspace corresponding to each non-zero eigenvalue is a finite-dimensional subspace of the space of smooth functions. As an application, we obtain a necessary and sufficient condition for the existence of a contact form with zero CR $Q$-curvature. |
| title | Analysis of the critical CR GJMS operator |
| topic | Differential Geometry Analysis of PDEs Complex Variables Spectral Theory 32V20, 35P05, 58J40 |
| url | https://arxiv.org/abs/2009.13813 |