The Ricci flow on surfaces with boundary

2012/09/11 by Jean C. Cortissoz, Cortissoz, Jean C., Alexander Murcia +1
Mathematics · #35K55 #53C44 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:35K55 #msc:53C44

paper · pdf · doi:10.48550/arxiv.1209.2386

Submitted version. Corrections and suggestions by referees have been incorporated

arxiv created 2016/03/10 · arxiv updated 2016/03/11

Abstract

We show for a non homogeneous boundary value problem for the Ricci flow on the disk that when the initial metric has positive curvature and the boundary is convex then the initial metric is deformed, via the normalized flow and along sequences of times, to a metric of constant curvature and totally geodesic boundary. We also show that when the geodesic curvature of the boundary is nonpositive and the metric is rotationally symmetric, the normalized version of the flow exists for all time.

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