Improved decay rate in a stability theorem for hyperbolic metrics

2023/06/13 by Jäckel, Frieder
#53C20 #53C25 #57K32 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2306.07722

Abstract

Recently, Ursula Hamenstädt and the author proved a stability result for finite volume hyperbolic metrics in dimension three that does not assume any upper volume bounds, but that requires an exponentially fine control of the metric in the thin part of the manifold. We use a bootstrap argument to extend the result allowing for a weaker exponential control of the metric. This is achieved by formulating an abstract axiomatic framework.

Related

• Volume Stability for Hyperbolic Manifolds and Applications to General Relativity
• Stability of Einstein metrics and effective hyperbolization in large Hempel distance
• Entropy and stability of hyperbolic manifolds
• A hyperbolic metric and stability conditions on K3 surfaces with ρ=1
• Intrinsic flat stability of the positive mass theorem for asymptotically hyperbolic graphical manifolds