Luca Battaglia, Sergio Cruz Blázquez, Angela Pistoia
Published 2023-05-16Version 1
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.
Prescribing almost constant curvatures on manifolds with boundary
Prescribing the Gaussian curvature in a subdomain of S^2 with Neumann boundary condition
The prescribed curvature flow on the disc
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