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arXiv · 2305.09622

Prescribing nearly constant curvatures on balls

Luca Battaglia·Sergio Cruz-Blázquez·Angela Pistoia
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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.

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Luca Battaglia, Sergio Cruz-Blázquez, Angela Pistoia. 2023-05-16. Prescribing nearly constant curvatures on balls. https://doi.org/10.1017/prm.2023.111

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