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arXiv · 2312.13011

Dynamical Stability and Instability of Poincar\'e--Einstein Manifolds

Klaus Kroencke·Louis Yudowitz
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Abstract

We prove dynamical stability and instability theorems for Poincar\'{e}-Einstein metrics under the Ricci flow. Our key tool is a variant of the expander entropy for asymptotically hyperbolic manifolds, which Dahl, McCormick and the first author established in a recent article. It allows us to characterize stability and instability in terms of a local positive mass theorem and in terms of volume comparison for nearby metrics.

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Klaus Kroencke, Louis Yudowitz. 2023-12-20. Dynamical Stability and Instability of Poincar\'e--Einstein Manifolds. https://arxiv.org/abs/2312.13011

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