Effective stability of negatively curved Einstein metrics in dimensions at least $4$

Frieder Jäckel

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arXiv · 2502.16692

Effective stability of negatively curved Einstein metrics in dimensions at least $4$

Frieder Jäckel

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Abstract

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.

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Frieder Jäckel. 2025-02-23. Effective stability of negatively curved Einstein metrics in dimensions at least $4$. https://arxiv.org/abs/2502.16692

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