Effective stability of negatively curved Einstein metrics in dimensions at least $4$
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | |
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| _version_ | 1866912792390402048 |
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| author | Jäckel, Frieder |
| author_facet | Jäckel, Frieder |
| contents | We show that if a closed manifold of dimension at least four admits a negatively curved metric that is almost Einstein in a suitable sense, then it admits a genuine Einstein metric of negative sectional curvature. Importantly, the pinching constant measuring the almost-Einstein condition neither depends on an upper bound for the diameter or volume, nor on a lower bound for the injectivity radius. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16692 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effective stability of negatively curved Einstein metrics in dimensions at least $4$ Jäckel, Frieder Differential Geometry 53C20, 53C25 We show that if a closed manifold of dimension at least four admits a negatively curved metric that is almost Einstein in a suitable sense, then it admits a genuine Einstein metric of negative sectional curvature. Importantly, the pinching constant measuring the almost-Einstein condition neither depends on an upper bound for the diameter or volume, nor on a lower bound for the injectivity radius. |
| title | Effective stability of negatively curved Einstein metrics in dimensions at least $4$ |
| topic | Differential Geometry 53C20, 53C25 |
| url | https://arxiv.org/abs/2502.16692 |