# Contractions and Isometries

## Bernd Kirchheim

### (Univ. Oxford)

Date: Oct 10, 2013, time: 15:30

Abstract. We discuss the class of strongly isometric maps, i.e. maps who preserve
the length of every curve, rectifiable or not. It is shown that these maps
are prevalent (in the topological sense) in the class of all contractions.
on Euclidean space. When considering a similar result on subset of
$R^n$,
the openness of the restriction operator with respect to the supremum
norm becomes crucial - several positive but also negative results
concerning this question are presented.