Prescribing nearly constant curvatures on balls
Analysis of PDEs
2025-06-11 v2 Differential Geometry
Abstract
In this paper we address two boundary cases of the classical Kazdan-Warner problem. More precisely, we consider the problem of prescribing the Gaussian and boundary geodesic curvature on a disk of R^2, and the scalar and mean curvature on a ball in higher dimensions, via a conformal change of the metric. We deal with the case of negative interior curvature and positive boundary curvature. Using a Ljapunov-Schmidt procedure, we obtain new existence results when the prescribed functions are close to constants.
Keywords
Cite
@article{arxiv.2305.09622,
title = {Prescribing nearly constant curvatures on balls},
author = {Luca Battaglia and Sergio Cruz-Blázquez and Angela Pistoia},
journal= {arXiv preprint arXiv:2305.09622},
year = {2025}
}
Comments
30 pages, accepted on Proc. Roy. Math. Soc. Edinburgh Sect. A