Curvature flows on four manifolds with boundary

2007/08/15 by Cheikh Birahim Ndiaye, Ndiaye, Cheikh Birahim
Mathematics · #35B33 #53A30 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0708.2029

openalex publication_date 2007/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a compact four dimensional smooth Riemannian manifold (M,g) with smooth boundary, we consider the evolution equation by Q-curvature in the interior keeping the T-curvature and the mean curvature to be zero and the evolution equation by T-curvature at the boundary with the condition that the Q-curvature and the mean curvature vanish. Using integral method, we prove global existence and convergence for the Q-curvature flow (resp T-curvature flow) to smooth metric of prescribed Q-curvature (resp T-curvature) under conformally invariant assumptions.

Citations

• Partial Differential Equations

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