https://neckpinch.com/authors/rasmus-jouttijarvi/New arXiv papers by Rasmus Jouttijärvi, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2607.05002/arxiv:2607.05002Mon, 06 Jul 2026 00:00:00 GMTRasmus Jouttijärvi — 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".Ricci flowEinstein metricsScalar curvatureStability & uniquenessBoundaries & non-compactPhysics https://neckpinch.com/papers/2403.09169/arxiv:2403.09169Thu, 14 Mar 2024 00:00:00 GMTRasmus Jouttijärvi — 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.Ricci flowEinstein metricsBoundaries & non-compact