On the Ricci flow on the rotationally symmetric two-ball

Details On the Ricci flow on the rotationally symmetric two-ball On the Ricci flow on the rotationally symmetric two-ball

2005-09-06

arxiv.org/abs/math/0509128v2

Mathematics

Differential Geometry

30 pages

Scientific paper

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.

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