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arXiv · 2502.15976

Prescribing curvatures on surfaces with conical singularities and corners

Luca Battaglia·Francisco Javier Reyes-Sanchez
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Abstract

This paper is concerned with the problem of prescribing Gaussian curvature and geodesic curvature in a compact surface with boundary with conical singularities and corners. Solutions are obtained using a new variational formulation, recently introduced for the regular counterpart of the problem and extended here to the singular case. As far as we know, this is the first result for the problem of prescribed curvatures in surfaces with singularities.

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Luca Battaglia, Francisco Javier Reyes-Sanchez. 2025-02-21. Prescribing curvatures on surfaces with conical singularities and corners. https://arxiv.org/abs/2502.15976

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