Daniel Ramos
CMAFCIO, ULisboa

Abstract: Every smooth closed surface admits a Riemannian metric of constant curvature, determined by its Euler characteristic. Surfaces with cone-like singularities (such as certain orbifolds) may fail to admit such constant curvature metrics. We propose a Ricci soliton metic as the canonical metric on these cases, and we prove that Ricci flow converges to such soliton metrics for any initial metric on closed surfaces with cone angles less than or equal to pi. The Ricci flow is an evolution equation introduced by R. Hamilton in 1982 and used by G. Perelman in 2002 to prove the Thurston geometrization of closed 3-manifolds. We use Perelman's techniques for conesingular closed surfaces and we discuss some open problems of the flow in open surfaces.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.