# Highly regular surjections from Euclidean domains to metric spaces

## Jeremy Tyson (Illinois University)

created by magnani on 16 Nov 2008

20 nov 2008

Abstract.

SEMINARIO DI ANALISI

17:00-18:00, Sala Riunioni (Dip. Matematica)

ABSTRACT. We study highly regular Peano type surjections from Euclidean cubes. We prove that every compact quasiconvex doubling metric space is the image of the n-dimensional compact cube under a surjection which is Holder, or Lipschitz if the dimension n'' is sufficiently large. As an application we prove that the Heisenberg group, equipped with its Carnot-Caratheodory metric, is the Lipschitz image of R5. This is joint work with Piotr Hajlasz.

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