The spectral geometry of hyperbolic and spherical manifolds: analogies and open problems
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915010785050624 |
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| author | Lauret, Emilio A. Linowitz, Benjamin |
| author_facet | Lauret, Emilio A. Linowitz, Benjamin |
| contents | The spectral geometry of negatively curved manifolds has received more attention than its positive curvature counterpart. In this paper we will survey a variety of spectral geometry results that are known to hold in the context of hyperbolic manifolds and discuss the extent to which analogous results hold in the setting of spherical manifolds. We conclude with a number of open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10950 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The spectral geometry of hyperbolic and spherical manifolds: analogies and open problems Lauret, Emilio A. Linowitz, Benjamin Differential Geometry 58J53 (Primary) 22C05, 58J50 (Secondary) The spectral geometry of negatively curved manifolds has received more attention than its positive curvature counterpart. In this paper we will survey a variety of spectral geometry results that are known to hold in the context of hyperbolic manifolds and discuss the extent to which analogous results hold in the setting of spherical manifolds. We conclude with a number of open problems. |
| title | The spectral geometry of hyperbolic and spherical manifolds: analogies and open problems |
| topic | Differential Geometry 58J53 (Primary) 22C05, 58J50 (Secondary) |
| url | https://arxiv.org/abs/2305.10950 |