Prescribing the Lorentzian mean curvature of a spacelike hypersurface, and the Born-Infeld model

Luciano Mari
(Universita degli Studi di Milano)

Abstract: The talk aims to introduce the reader to the existence and regularity problem 
for spacelike hypersurfaces in Lorentz-Minkowski space whose mean curvature is a 
prescribed measure. The class includes, for instance, maximal surfaces with point singularities. 
Motivation comes from General Relativity and from the electrostatic Born-Infeld theory, 
according to which the graph function represents the electric potential and its mean 
curvature the given charge distribution. Various open problems will be discussed. 

The talk is based on joint works with J. Byeon, N. Ikoma, A. Malchiodi and L. Maniscalco.