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Under the definition of Ricci curvature bounded below for Alexandrov spacesintroduced by Zhang-Zhu, we generalize a result by Colding that an ndimentional manifold with Ricci curvature greater or equal to n minus 1 andvolume close to that of the unit n sphere is close (in the Gromov-Hausdorffdistance) to the sphere, from the case of Riemannian manifolds to the case ofAlexandrov spaces, with an additional assumption, roughly speaking, that therough volume of the set of short cut points is small, following the basic ideain the Riemannian case with necessary modifications because of the only almosteverywhere second differentiability of distance functions.

Shape of Alexandrov spaces with positive Ricci curvature