2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/51001A proof is given of Polyakov conjecture about the auxiliary parameters of the SU(1,1) Riemann-Hilbert problem for general elliptic singularities. Such a result is related to the uniformization of the the sphere punctured by n conical defects. Its relevance to the hamiltonian structure of 2+1 dimensional gravity in the maximally slicing gauge is stressed.Talk by P. Menotti at Int. Europhysics Conference on High Energy Physics, Budapest 12-18 July 2001, 5 pages latexHigh Energy Physics - Theorytext