Seminari del Dipartimento di Matematica
Università di Bologna

06 Mar 2014
seminario di analisi matematica
Dimension distortion by Sobolev mappings on the Heisenberg group
Prof. Kevin Wildrick (Université de Fribourg), ospite di Annalisa Baldi nell’ambito di un progetto GNAMPA
The Heisenberg group is equipped with a foliation by horizontal lines that differs substantially from the standard foliation of Euclidean space by lines. We investigate the behavior of Sobolev mappings on this foliation. It is a fundamental property of Sobolev mappings that they are absolutely continuous on almost every line; we estimate the quantity of lines whose image under a Sobolev mapping has dimension at least a fixed number d>1.