Abstract
Hausdorff dimension and higher order Sobolev maps
Bernd Kirchheim
Universität Leipzig
We investigate how Hausdorff dimension and measure behave
if a set is mapped by a (exact representative of) map in a
Sobolev space which embedds into the continuous functions (or
equivalently L-infinity). The underlying results on decomposing
the maps into pieces of appropriate Hoelder or Lipschitz continuity
allow to establish essentially sharp versions of area formulae.
This is joint work with G. Alberti, M. Csornyei and E. D'Aniello.
if a set is mapped by a (exact representative of) map in a
Sobolev space which embedds into the continuous functions (or
equivalently L-infinity). The underlying results on decomposing
the maps into pieces of appropriate Hoelder or Lipschitz continuity
allow to establish essentially sharp versions of area formulae.
This is joint work with G. Alberti, M. Csornyei and E. D'Aniello.