arXiv subjects

Rasmus Jouttijärvi

Publications and source records attributed to Rasmus Jouttijärvi.

3 recordsLinked to original sources

arXiv2026

On the Stability of Einstein Manifolds with Boundary

We study the stability problem for Einstein manifolds with boundary with respect to the Einstein-Hilbert action. The geometric boundary conditions we are using arise naturally from studying the calculus of variations associated with Ricci flow. Upon the introduction of a boundary, the space of TTg tensors no longer arise naturally as the defining space for the stability condition. Thus we must settle for the larger subspace of tensors preserving the scalar curvature, the total volume and the Bianchi gauge condition, which we call the space of TVg tensors. As a test-case, we shall discuss stability of the Riemannian Schwarzschild anti-deSitter family of metrics; a problem known as "a Black hole in a box".

math.DG↗

arXiv2026

Static Vacuum Spacetimes with $Λ<0$ as Attractors of the Ricci-Harmonic Flow

We prove dynamical stability and instability theorems for asymptotically hyperbolic static solutions of Einstein's equation with $Λ<0$, viewed as self-similar solutions of the Ricci-harmonic flow. More precisely, we show that static metrics are dynamically stable if and only if a positive mass type theorem holds for nearby metrics. Our key tool is a new variant of the expander entropy for the Ricci-harmonic flow.

math.DG↗

arXiv2024

Novel Boundary Conditions for the Ricci Flow

If we want to deform a compact Riemannian manifold with boundary using Ricci flow, we first need to decide on appropriate boundary conditions. We would like these conditions to reflect the geometric nature of the flow and allow for a variety of initial data. Importantly, the conditions should be compatible with the expected evolution of Einstein metrics. We propose it is natural to choose those conditions, for which the first variation of certain functionals, such as the Einstein-Hilbert action and Perelmans lambda-functional, does not admit a boundary term. We provide a proof of the short term existence of solutions of the initial boundary value problem, under these conditions.

math.DG↗