在圆盘上给定高斯曲率与测地曲率
偏微分方程分析
2018-06-19 v1
摘要
在本文中,我们考虑通过度量的共形变换分别在圆盘及其边界上给定高斯曲率与测地曲率的问题。这将我们引向一个带有非线性 Neumann 边界条件的 Liouville 型方程。我们通过在变分框架中设定该问题来处理存在性问题,该框架在文献中似乎是全新的。我们能够在对称性假设下找到极小化子。
引用
@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}
}
备注
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)