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In this article, we study the problem (sometimes called the Berger-Nirenberg problem) of prescribing the curvature on a Riemann surface (that is on an oriented surface equipped with a conformal class of Riemannian metrics).
Nicolas Boumal, Christopher Arnold Criscitiello
Pedro Miguel Nunes Pereira de Almeida Reis, Celestin Vallat, Tian Chen, Tomohiko Sano, Samuel Jean Bernard Poincloux