Proportional concentration phenomena on the sphere (Q1860714)

Let \(E_k\) be a \(k\)-dimensional subspace of \(\mathbb{R}^n\) and \(\mu((E_k)_\varepsilon)\) the Haar measure on the sphere \(\mathbb{S}^{n-1}\) of the set of points within a geodesic distance smaller than \(\varepsilon\) of \(E_k\). In the paper under review, there are given various asymptotic estimates for \(\mu((E_k)_\varepsilon)\) which are applied to the problem of projections of points on the sphere, and to the duality of the entropy numbers conjecture. The details are too technical to be stated here.