Mathematics

Title: Area Functional and Semicartesian Parametrization: Facts, Hopes and open Problems

Abstract: In this talk I will introduce the area functional for L^1 functions from an open domain of R^2 with values in R^2 and I will recall some known results, properties, and problems. For particular discontinuous functions jumping on a regular curve, we conjecture that the singular contribution of the area functional can be computed by solving a Plateau's problem in R^3 and by finding a particular parametrization of the solution, that we call "semicartesian". I will present some results providing an upper bound for the area functional and I will discuss possible outlooks.

This seminar is part of the AJS series of seminars.