University College, UK

Tue 24 May 2016, 3:30pm
ESB 2012

Ricci flow from metrics with isolated conical singularities

ESB 2012
Tue 24 May 2016, 3:30pm4:30pm
Details
Abstract: Let (M,g_0) be a compact ndimensional Riemannian manifold with a finite number of singular points, where at each singular point the metric is asymptotic to a cone over a compact (n1)dimensional manifold with curvature operator greater or equal to one. We show that there exists a smooth Ricci flow starting from such a metric with curvature decaying like C/t. The initial metric is attained in GromovHausdorff distance and smoothly away from the singular points. To construct this solution, we desingularize the initial metric by glueing in expanding solitons with positive curvature operator, each asymptotic to the cone at the singular point, at a small scale s. Localizing a recent stability result of DeruelleLamm for such expanding solutions, we show that there exists a solution from the desingularized initial metric for a uniform time T>0, independent of the glueing scale s. The solution is then obtained by letting s>0. We also show that the so obtained limiting solution has the corresponding expanding soliton as a forward tangent flow at each initial singular point. This is joint work with P. Gianniotis.
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