In this note, we provide several lower bounds for the volume of a geodesic ball within the injectivity radius in a 3‐dimensional Riemannian manifold assuming only upper bounds for the Ricci curvature.

中文翻译：

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三维的体积下界与Ricci曲率的上限

在本注释中，我们假设3维黎曼流形中的注射半径内的测地线球的体积有几个下限，而仅假定Ricci曲率的上限。