Professor Marianna Csörnyei

Lipschitz maps, problems concerning the complexity of sets and functions.e.g. does there exist a set on the plane whose measure function is Lipschitz in every strip?

Problems in Analysis with Set Theoretic flavour, consistency problems. Is it consistent that the covering of the Hilbert cube requires more Cantor sets than that of the interval? Is every Borel mapping of a metric space X to a metric space Y of bounded class?

Hausdorff measures and dimensions. Does there exist a compact set on the plane that intersects all the lines in a finite set, but has non-sigma-finite one dimensional measure? Is it true that a.e. line through a.e. point of a purely unrectifiable 1-set intersects the set at finitely many points?

Geometry of Banach spaces, measure theoretic problems. Does Vitali Covering Theorem hold in the space of null sequences? Are the ball and the sphere of the Hilbert space Lipschitz isomorphic?

This page was last modified on April 15, 2011 by Helen Higgins