Variation of cone metrics on Riemann surfaces (Q2568957)

The authors study the hyperbolic metrics with conical singularities on compact Riemann surfaces and consider the variation of the hyperbolic conical metric in holomorphic families, and introduce a generalized Weil-Petersson metric. They discuss the variational properties of the unique conical metric of constant curvature \(-1\) associated to a compact Riemann surface together with a weighted divisor.