Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Existence of H-surfaces in cones and their representation as radial graphs

Alessandro Iacopetti

created by risa on 29 Jan 2016

4 feb 2016 -- 14:15

Aula di Consiglio, Dip.Matematica, Università "La Sapienza", Roma

Abstract.

In this talk we show some recent results concerning the Plateau problem for disc-type surfaces with prescribed mean curvature H, spanning a given Jordan curve and contained in a convex cone. Under some growth condition on H we prove existence of a solution X characterized as minimizer of the energy associated to the problem. Moreover, under a suitable monotonicity assumption on H, we show that if the Jordan curve has injective radial projection on the unit sphere, then X is the radial graph of a mapping on the interior domain of the unit sphere bounded by the radial projection of the curve. These results are contained in a joint work with Paolo Caldiroli (Università di Torino) see arXiv:1512.03789.

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