We prove a compactness theorem for metrics with bounded integral curvature on a fixed closed surface $\unicode[STIX]{x1D6F4}$. As a corollary we obtain a new convergence result for sequences of metrics with conical singularities, where an accumulation of singularities is allowed.

中文翻译：

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有界积分曲率曲面的紧致性定理

我们证明了在固定闭合曲面上具有有界积分曲率的度量的紧致性定理$\unicode[STIX]{x1D6F4}$. 作为推论，我们获得了具有锥形奇点的度量序列的新收敛结果，其中允许奇点的累积。