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arXiv · 2007.06724

The Nirenberg Problem for Conical Singularities

Lisandra Hernandez-Vazquez
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Abstract

We propose a new approach to the question of prescribing Gaussian curvature on the 2-sphere with at least three conical singularities and angles less than $2\pi$, the main result being sufficient conditions for a positive function of class at least $C^2$ to be the Gaussian curvature of such a conformal conical metric on the round sphere. Our methods particularly differ from the variational approach in that they don't rely on the Moser-Trudinger inequality. Along the way, we also prove a general precompactness theorem for compact Riemann surfaces with at least three conical singularities and angles less than 2$\pi$.

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Lisandra Hernandez-Vazquez. 2020-07-13. The Nirenberg Problem for Conical Singularities. https://arxiv.org/abs/2007.06724

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