IMPA - The Institute for Pure and Applied Mathematics

In the sixties, Jenkins and Serrin proved a celebrated theorem about minimal graphs in the Euclidean 3-space with infinite boundary values. After reviewing the classical theory, we show how to solve the Jenkins-Serrin problem in a 3-manifold carrying a Killing vector field. This is a joint work with A. Del Prete and J. M. Manzano.

Modelling non-separating surfaces as level sets of solutions to an elliptic equation, requires thinking of these as sections of a line bundle rather than as usual functions. This perspective introduces an arena full of interesting new problems for elliptic functionals. In this talk I would like to spend quite some time discussing these variety of open problems and briefly discuss my recent work with Marco Badran and Manuel Del Pino on Plateau’s problem.