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Overdetermined problems and constant mean curvature surfaces in cones

Ponente: Filomena Pacella
Tipo de Evento: Investigación
Cuándo 20/02/2019 de 12:00 a 13:00 Salón de seminarios "Graciela Salicrup" vCal iCal

Abstract:

After recalling classical results about characterizations of spheres and balls in the euclidean space, I will present some recent results about:

i) Characterization of domains in cones which admit a solution of a partial overdetermined problem of Serrin type.

ii) Characterization of some constant mean curvature surfaces with boundary.

As in the classical case of closed surfaces, the above questions are strictly related and we show that under some hypotheses on the cone or on the surface, the domains and surfaces characterized by i) and ii) are spherical sectors and spherical caps (respectively) centered at the vertex of the cone.

Finally, connections with a relative isoperimetric inequality will be described.

The results have been obtained in collaboration with Giulio Tralli (University of Padova, Italia)