Calculus of Variations and Geometric Measure Theory

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.