Calculus of Variations and Geometric Measure Theory

S. Cruz Blázquez - D. Ruiz

Prescribing Gaussian and geodesic curvature on the disk

created by cruzblázquez on 20 Apr 2018
modified on 20 Jun 2018


Accepted Paper

Inserted: 20 apr 2018
Last Updated: 20 jun 2018

Journal: Advanced Nonlinear Studies
Pages: 18
Year: 2018

ArXiv: 1806.06292 PDF


In this paper we consider the problem of prescribing the Gaussian and geodesic curvature on a disk and its boundary, respectively, via a conformal change of the metric. This leads us to a Liouville-type equation with a nonlinear Neumann boundary condition. We address the question of existence by setting the problem in a variational framework which seems to be completely new in the literature. We are able to find minimizers under symmetry assumptions.

Keywords: Variational methods, Moser-Trudinger inequality, Prescribed Gaussian curvature problem