| Abstract: |
| I will consider the problem of prescribing the Gaussian curvature (under pointwise conformal change of the metric) on surfaces with conical singularities. This question has been first raised by Troyanov [TAMS,1991] and it is a generalization of the Kazdan-Warner problem for regular surfaces, known as the Nirenberg problem on the sphere.
From the analytical point of view, this amounts to solve a singular Liouville-type equation on the surface.\
Initially, in the supercritical regime, only the case of positive prescribed Gaussian curvature has been attacked. In this talk I will present some new results (obtained in collaboration with T. D`Aprile, I. Ianni, S. Kallel, R. L\`{o}pez-Soriano and D. Ruiz) concerning the sign-changing case. |
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