2024/03/14 by Rasmus Jouttijärvi, Jouttijärvi, Rasmus
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows
paper · pdf · doi:10.48550/arxiv.2403.09169
openalex publication_date 2024/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.