We show that any closed manifold with a metric of nonpositive curvature that admits either a single point rank condition or a single point curvature condition has positive simplicial volume. We use this to provide a differential geometric proof of a conjecture of Gromov in dimension three.

中文翻译：

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关于非正弯曲流形的单纯体积的一些评述

我们表明，任何具有非正曲率度量的封闭流形，其允许单点秩条件或单点曲率条件都具有正单纯体积。我们用它来提供第三维格罗莫夫猜想的微分几何证明。