Work

Dynamical stability and instability of Poincaré–Einstein manifolds

Year: 2024

Type: article

Abstract: 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.

Source: Calculus of Variations and Partial Differential Equations

DOI: 10.1007/s00526-024-02890-7

Authors: Klaus Kröncke, Louis Yudowitz

Institution: KTH Royal Institute of Technology

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Göran Gustafssons Stiftelser, Kungliga Tekniska Högskolan