Some new embedding results for subRiemannian manifolds

Enrico Le Donne

(ETH Zurich)

Event: ERC School on Analysis in Metric Spaces and Geometric Measure Theory

Date: Jan 13, 2011, time: 14:30

Place: Centro De Giorgi, Scuola Normale Superiore

Abstract. SubRiemannian manifolds are particular metric spaces which are generalizations of Riemannian manifolds. Whitney Embedding Theorem implies that any Riemannian manifold can be biLipschitz embedded into an Euclidean space. However, this conclusion does not hold anymore if the manifold is only SubRiemannian. The main purpose of the talk is to explain that, nevertheless, the analogue of Nash Embedding Theorem is
still valid for subRiemannian manifolds. Time permitting, we will mention some other embedding results, some of which are in collaboration with Urs Lang.