Metrics of constant curvature 1 with three conical singularities on   2-sphere
  A necessary and sufficient condition for the existence and uniqueness of a conformal metric on 2-sphere of constant curvature 1 and with three conical singularities of prescribed order is given. 
Masaaki Umehara (Osaka Univ.) and Kotaro Yamada (Kumamoto Univ.)