Calculus of Variations and Geometric Measure Theory

Besicovitch-Federer projection theorem is false in every infinite dimensional Banach space

David Bate (University of Warwick)

created by ambrosio on 02 May 2018

14 may 2018 -- 11:00   [open in google calendar]

Scuola Normale Superiore, Aula Marie Curie


The Besicovitch-Federer projection theorem is a fundamental result of classical geometric measure theory and it is natural to ask if generalisations exist outside of the Euclidean setting. We will demonstrate its failure in Hilbert space by constructing a purely unrectifiable set of finite $\mathcal H^1$ measure whose image under every (non-zero) continuous linear function has positive Lebesgue measure. Time permitting, I will discuss how the counter example may be generalised to any infinite dimensional separable Banach space. This is joint work with Marianna Csörnyei and Bobby Wilson.