A sup × inf-type inequality for conformal metrics on Riemann surfaces with conical singularities

A sup × inf-type inequality is proved for the regular part of conformal factors for Riemannian metrics on surfaces with conical singularities of positive order α > 0 . The proof is based on the explicit representation formula for solutions of the singular Liouville equation and generalizes to the singular case an argument by I. Shafrir.