Prescribing nearly constant curvatures on balls

Fuente: arXiv
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Main Authors: Battaglia, Luca, Cruz-Blázquez, Sergio, Pistoia, Angela
Format: Preprint
Published: 2023
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author Battaglia, Luca
Cruz-Blázquez, Sergio
Pistoia, Angela
author_facet Battaglia, Luca
Cruz-Blázquez, Sergio
Pistoia, Angela
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2305_09622
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Prescribing nearly constant curvatures on balls
Battaglia, Luca
Cruz-Blázquez, Sergio
Pistoia, Angela
Analysis of PDEs
Differential Geometry
35J25, 58J32
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.
title Prescribing nearly constant curvatures on balls
topic Analysis of PDEs
Differential Geometry
35J25, 58J32
url https://arxiv.org/abs/2305.09622