The Minkowski problem and surfaces of constant curvature
Rabah Souam Université Paris VII
We classify the family of positive constant curvature surfaces in whose extrinsic conformal structure is biholomorphic to a planar circular domain, and whose Gauss map is a diffeomorphism onto a finitely punctured sphere. We give applications to the generalized Minkowski problem, the existence of harmonic diffeomorphisms between certain domains of , the existence of capillary surfaces in , and the space of solutions to a Hessian equation of Monge-Ampère type.
Joint work with Antonio Alarcón.