We prove that a proper geodesic metric space has non-positive curvature in the sense of Alexandrov if and only if it satisfies the Euclidean isoperimetric inequality for curves. Our result extends to non-geodesic spaces and non-zero curvature bounds.

中文翻译：

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曲率上限的等周表征

我们证明了一个适当的测地线度量空间在亚历山德罗夫的意义上具有非正曲率，当且仅当它满足曲线的欧几里德等周不等式。我们的结果扩展到非测地线空间和非零曲率边界。