Prescribing Gaussian and geodesic curvature on disks
Abstract
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
Cite
@article{arxiv.1806.06292,
title = {Prescribing Gaussian and geodesic curvature on disks},
author = {S. Cruz-Blázquez and D. Ruiz},
journal= {arXiv preprint arXiv:1806.06292},
year = {2018}
}
Comments
18 pages, 1 figure. S. C-B is a student of the INdAM Doctoral Programme in Mathematics and/or Applications Cofunded by Marie Sklodowska-Curie Actions (INdAM-DP-COFUND-2015) and he is supported by the Marie Sklodowska-Curie fellowship of the Istituto Nazionale di Alta Matematica number 713485. D. R. have been supported by the Feder-Mineco Grant MTM2015-68210-P and by J. Andalucia (FQM116)