Special Session 121: Recent developments on nonlinear geometric PDEs

A mean field approach for the double curvature prescription problem

Luca Battaglia
Universita degli Studi Roma Tre
Italy
Co-Author(s):    Rafael Lopez-Soriano
Abstract:
We establish a new mean field-type formulation to study the problem of prescribing Gaussian and geodesic curvature on compact surfaces, which is equivalent to a Liouville-type PDE with nonlinear Neumann conditions. We provide three different existence results in the case of positive, zero and negative Euler characteristics.