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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2207.13498 |
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| _version_ | 1866913497178177536 |
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| author | Jung, Junehyuk Zelditch, Steve |
| author_facet | Jung, Junehyuk Zelditch, Steve |
| contents | We prove that the real parts of equivariant (but non-invariant) eigenfunctions of generic bundle metrics on nontrivial principal $S^1$ bundles over manifolds of any dimension have connected nodal sets and exactly 2 nodal domains. This generalizes earlier results of the authors in the $3$-dimensional case. The failure of the results on for non-free $S^1$ actions is illustrated on even dimensional spheres by one-parameter subgroups of rotations whose fixed point set consists of two antipodal points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_13498 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | $2$-nodal domain theorems for higher dimensional circle bundles Jung, Junehyuk Zelditch, Steve Spectral Theory Analysis of PDEs We prove that the real parts of equivariant (but non-invariant) eigenfunctions of generic bundle metrics on nontrivial principal $S^1$ bundles over manifolds of any dimension have connected nodal sets and exactly 2 nodal domains. This generalizes earlier results of the authors in the $3$-dimensional case. The failure of the results on for non-free $S^1$ actions is illustrated on even dimensional spheres by one-parameter subgroups of rotations whose fixed point set consists of two antipodal points. |
| title | $2$-nodal domain theorems for higher dimensional circle bundles |
| topic | Spectral Theory Analysis of PDEs |
| url | https://arxiv.org/abs/2207.13498 |