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Shu-Yu Hsu

2011-10-20
15:00:00 - 16:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)

In this talk I will prove the existence of the minimizer of an isoperimetric ratio for a metric on the plane with finite total area. I will also show how this result can be used to study the singularity properties of Ricci flow on complete $\R^2$. This existence of minimizer result is assumed and used without proof by P.~Daskalopoulos and R.~Hamilton in their proof of the lower and upper estimates for the width and maximum scalar curvature of the maximal solution of Ricci flow on complete $\R^2$.