Peano continua from a point of view of analysis

Piotr Hajlasz, 
Department of Mathematics, University of Pittsburgh

The classical theorem of Hahn and Mazurkiewicz characterizes metric
spaces that are continuous images of an interval, or equivalently, a
cube. In the talk I will discuss recent generalizations of the
Hahn-Mazurkiewicz theorem to the case in which we require higher
regularity of a mapping: Holder continuity, Lipschitz continuity,
Sobolev regularity or even higher order differentiability. The talk is
based on a joint work with Jeremy Tyson.