On the Ricci flow on the rotationally symmetric two-ball

2005/09/06 by Jean Cortissoz, Cortissoz, Jean
Mathematics · #37E35 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:37E35

paper · pdf · doi:10.48550/arxiv.math/0509128

30 pages

arxiv created 2007/04/17 · arxiv updated 2009/12/01

Abstract

In this paper we study a boundary value problem for the Ricci flow in the two dimensional ball endowed with a rotationally symmetric metric. We show short and long time existence results. We construct families of metrics for which the flow uniformizes the curvature along a sequence of times. Finally we show that if the initial metric has positive Gaussian curvature and the boundary positive geodesic curvature then the flow uniformizes de curvature along a sequence of times.

Related

• Rotationally symmetric Ricci Flow on ℝⁿ⁺¹
• The Ricci flow on surfaces with boundary
• Ricci Flow of regions with curvature bounded below in dimension three
• A local curvature estimate for the Ricci flow
• Another proof of the local curvature estimate for the Ricci flow