A quantitative version of Steinhaus’ theorem for compact, connected, rank-one symmetric spaces
Let $d_1$, $d_2$, ... be a sequence of positive numbers that converges to zero. A generalization of Steinhaus' theorem due to Weil implies that, if a subset of a homogeneous Riemannian manifold has no pair of points at distances $d_1$, $d_2$, ... from each other, then it has to have measure zero. We present a quantitative version of this result for compact, connected, rank-one symmetric spaces, by showing how to choose distances so that the measure of a subset not containing pairs of points at these distances decays exponentially in the number of distances.
|THEME||Logistics (theme 3)|
|Publisher||Cornell University Library|
|Series||arXiv.org e-Print archive|
|Project||Spinoza prijs Lex Schrijver|
de Oliveira Filho, F.M, & Vallentin, F. (2010). A quantitative version of Steinhaus’ theorem for compact, connected, rank-one symmetric spaces. arXiv.org e-Print archive. Cornell University Library .