Conical metrics on Riemann surfaces, II: spherical metrics

Abstract

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

Final version accepted by Int. Math. Res. Not

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Cited by in corpus (5)

• Rigidity of a family of spherical conical metrics
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• Cone spherical metrics and stable vector bundles
• Spherical conical metrics and harmonic maps to spheres
• Exotic vortices and twisted holomorphic maps