# Ievgen Bilokopytov

## The Dilation In Different Settings

Date Friday, May 2, 2014

The dilation of a map (i.e. the Lipschitz constant) is a basic concept from the theory of metric spaces. However it becomes much more useful in more specific situations. In particular, several corollaries from Arzela-Ascoli theorem will be considered. We will focus on the case of the metric spaces with intrinsic metric including smooth manifolds with Riemannian metric.