Esta es una nueva iniciativa del Departamento de Ingeniería Matemática que tiene como objetivo que todas y todos los profesores y estudiantes de postgrado del departamento podamos juntarnos en un ambiente descontraído y matemáticamente saludable una vez al mes. El coloquio DIM se realizará los últimos martes de cada mes a las 16:30, durará una hora y tendrá un cóctel al finalizar.
Para la primera sesión, les pedimos reservar la fecha del 25 de Abril a las 16:30, donde recibiremos a Filomena Pacella (La Sapienza University of Rome) en la sala de seminarios DIM del 5o piso Beauchef 851.
Title: CONSTANT MEAN CURVATURE SURFACES AND OVERDETERMINED PROBLEMS IN CONES
Abstract: I will discuss two classical problems in Geometry and Analysis: the first one is the characterization of constant mean curvature surfaces and the second one is the related question of studying domains which admit solutions of overdetermined problems.
After recalling the classical results of A.D.Alexandrov (1958, 1962) and J.Serrin (1971) I will present some recent developments on the characterization of constant mean curvature surfaces with boundary in cones and on the parallel question of characterizing domains inside a cone which admit a solution of an overdetermined problem.
The relation between the two topics and an isoperimetric inequality will be discussed. It will be shown that the convexity of the cone plays a role in obtaining symmetry results or in the construction of counterexamples.