On the filling radius of positively curved Alexandrov spaces
The notion of filling radius was introduced in [\textit{M. Gromov}, J. Differ. Geom. 18, 1--147 (1983; Zbl 0515.53037)]. In the paper under review, the author proves that if a positively curved closed Alexandrov space \(X\) is not isometric to the round sphere, then the filling radius of \(X\) is less than the round sphere's filling radius. This result generalizes the theorem of \textit{F. H. Wilhelm jun.} [Invent. Math. 107, No. 3, 653--668 (1992; Zbl 0729.53044)] for positively curved Riemannian manifolds.
scientific article; zbMATH DE number 6134697