30 oct 2017 -- 14:15
Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma
Abstract.
For every compact connected surface with negative Euler characteristic Koebe and Poincaré proved the existence and uniqueness of a metric of finite area and curvature -1 in each conformal class. McOwen and Troyanov proved an analogous result for metrics with prescribed conical behavior at given marked points. The analogous question for metrics of curvature 1 is subtler: in a small range existence and uniqueness still holds (Troyanov), in another range existence holds but uniqueness fails (Bartolucci-De Marchis-Malchiodi). The aim of this talk is to discuss some results of existence and non-existence of metrics of curvature 1 on surfaces with conical singularities. This is joint work with Dmitri Panov.