Dynamical stability and instability of Poincaré–Einstein manifolds: Dynamical stability and instability of Poincaré–Einstein manifolds

We prove dynamical stability and instability theorems for Poincaré–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 characteriz...

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Bibliographic Details
Published in:Calculus of variations and partial differential equations 2025, Vol.64 (1)
Main Authors: Kröncke, Klaus, Yudowitz, Louis
Format: Article
Language:English
Subjects:
Analysis
Asymptotic series
Calculus of Variations and Optimal Control
Optimization
Control
Manifolds
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Stability
Systems Theory
Theorems
Theoretical
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Summary:We prove dynamical stability and instability theorems for Poincaré–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.
ISSN:0944-2669
1432-0835
1432-0835
DOI:10.1007/s00526-024-02890-7