Conical Metrics on Riemann Surfaces, II: Spherical Metrics

Abstract We continue our study, initiated in [34], of Riemann surfaces with constant curvature and isolated conic singularities. Using the machinery developed that earlier paper extended configuration families simple divisors, we study existence deformation theory for spherical metrics some or all cone angles greater than $2\pi $. Deformations are obstructed precisely when number $2$ lies spectrum Friedrichs extension Laplacian. Our main result is that, this case, it possible to find a smooth local moduli space solutions by allowing points split. This analytic fact reflects geometric constructions [37, 38].