Blow-up analysis of conformal metrics of the disk with prescribed Gaussian and geodesic curvatures

This paper is concerned with the compactness of metrics of the disk with prescribed Gaussian and geodesic curvatures. We consider a blowing-up sequence of metrics and give a precise description of its asymptotic behavior. In particular, the metrics blow-up at a unique point on the boundary and we ar...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2020-04
Main Authors: Jevnikar, Aleks, López-Soriano, Rafael, Medina, María, Ruiz, David
Format: Article
Language:English
Subjects:
Asymptotic properties
Boundary conditions
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This paper is concerned with the compactness of metrics of the disk with prescribed Gaussian and geodesic curvatures. We consider a blowing-up sequence of metrics and give a precise description of its asymptotic behavior. In particular, the metrics blow-up at a unique point on the boundary and we are able to give necessary conditions on its location. It turns out that such conditions depend locally on the Gaussian curvatures but they depend on the geodesic curvatures in a nonlocal way. This is a novelty with respect to the classical Nirenberg problem where the blow-up conditions are local, and this new aspect is driven by the boundary condition.
ISSN:2331-8422
DOI:10.48550/arxiv.2004.14680