Proof of Polyakov conjecture for general elliptic singularities

TL;DR

This paper proves Polyakov's conjecture regarding accessory parameters in the SU(1,1) Riemann-Hilbert problem for elliptic singularities, highlighting its significance in 2+1 dimensional gravity.

Contribution

It provides a rigorous proof of Polyakov's conjecture for general elliptic singularities, extending previous results in the field.

Findings

Proof of Polyakov's conjecture established

Connection to 2+1 dimensional gravity emphasized

General elliptic singularities addressed

Abstract

A proof is given of Polyakov conjecture about the accessory parameters of the SU(1,1) Riemann-Hilbert problem for general elliptic singularities on the Riemann sphere. Its relevance to 2+1 dimensional gravity is stressed.