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
$\mathbb {R}^2$
, 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 presc… Show more
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