Analytic torsion for fibred boundary metrics and conic degeneration
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915455944359936 |
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| author | Lye, Jørgen Olsen Vertman, Boris |
| author_facet | Lye, Jørgen Olsen Vertman, Boris |
| contents | We study the renormalized analytic torsion of complete manifolds with fibred boundary metrics, also referred to as $ϕ$-metrics. We establish invariance of the torsion under suitable deformations of the metric, and establish a gluing formula. As an application, we relate the analytic torsions for complete $ϕ$- and incomplete wedge-metrics. As a simple consequence we recover a result by Sher and Guillarmou about analytic torsion under conic degeneration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic torsion for fibred boundary metrics and conic degeneration Lye, Jørgen Olsen Vertman, Boris Differential Geometry Analysis of PDEs Spectral Theory 58J52, 35K08, 53C21 We study the renormalized analytic torsion of complete manifolds with fibred boundary metrics, also referred to as $ϕ$-metrics. We establish invariance of the torsion under suitable deformations of the metric, and establish a gluing formula. As an application, we relate the analytic torsions for complete $ϕ$- and incomplete wedge-metrics. As a simple consequence we recover a result by Sher and Guillarmou about analytic torsion under conic degeneration. |
| title | Analytic torsion for fibred boundary metrics and conic degeneration |
| topic | Differential Geometry Analysis of PDEs Spectral Theory 58J52, 35K08, 53C21 |
| url | https://arxiv.org/abs/2403.04402 |