Abstract
Here we are concerned with the compactness of metrics on 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.
Citation
Aleks Jevnikar. Rafael López-Soriano. María Medina. David Ruiz. "BLOW-UP ANALYSIS OF CONFORMAL METRICS OF THE DISK WITH PRESCRIBED GAUSSIAN AND GEODESIC CURVATURES." Anal. PDE 15 (8) 1897 - 1931, 2022. https://doi.org/10.2140/apde.2022.15.1897
Information