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Abstract
LetM be a compact manifold of dimension greater than four. Denote byRiem(M) the space of Riemannian structures onM (i.e. of isometry classes of Riemannian metrics onM) endowed with the Gromov-Hausdorff metric. LetRieme(M) ⊂Riem(M) be its subset formed by all Riemannian structuresμ such that vol(μ)=1 andinj(μ) ≥e, whereinj(μ) denotes the injectivity radius ofμ.
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