The minimal volume of a smooth manifold the infimum of the set of volumes of compatible complete riemannian metrics having sectional curvatures between $ -1 $ and $ 1 $. It was conjectured by Gromov and proved by Bavard and Pansu that the minimal volume of the plane equals $ 2 \pi (1+\sqrt{2}) $. We offer an alternative proof of this result, and describe some related geometric inequalities.
J. Austral. Math. Soc. 55 (1993) 23-40.