A 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.Comment: Talk by P. Menotti at Int. Europhysics Conference on High Energy
Physics, Budapest 12-18 July 2001, 5 pages late
