Bate: Purely unrectifiable metric spaces and perturbations of Lipschitz functions
Bate: We give characterisations of purely $n$-unrectifiable subsets $S$ of a complete metric space $X$ with finite Hausdorff $n$-measure by studying arbitrarily small perturbations of Lipschitz functions $f\colon X \to R^m$. In one such characterisation it is shown that, if $S$ has positive lower density almost everywhere, a typical $f$ (with respect to the supremum norm) has ${\mathcal H}^n(f(S))=0$. Conversely, if $E\subset X$ is $n$-rectifiable with ${\mathcal H}^n(E)>0$, a typical $f$ has ${\mathcal H}^n(f(E))>0$. These results provide a replacement for the Besicovitch-Federer projection theorem in arbitrary metric spaces, which is known to be false outside of Euclidean spaces. http://cvgmt.sns.it/seminar/633/
When
Wed May 16, 2018 3pm – 4pm Coordinated Universal Time
Where
Sala Seminari Dipartimento di Matematica di Pisa (map)
