Inserted: 3 nov 2020
Last Updated: 3 nov 2020
We study conformal metrics with prescribed Gaussian curvature on surfaces with conical singularities and geodesic boundary in supercritical regimes. Exploiting a variational argument, we derive a general existence result for surfaces with at least two boundary components. This seems to be the first result in this setting. Moreover, we allow to have conical singularities with both positive and negative orders, that is cone angles both less and greater than $2\pi$.
Keywords: Variational methods, Prescribed Gaussian curvature, conformal metrics, conical singularities, geodesic boundary