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SUMMARY:David Bate (University of Warwick)
DTSTART:20210721T121500Z
DTEND:20210721T131500Z
DTSTAMP:20260423T023934Z
UID:NCTS-GMT/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NCTS-GMT/5/"
 >A non-linear Besicovitch–Federer projection theorem for metric spaces</
 a>\nby David Bate (University of Warwick) as part of NCTS international Ge
 ometric Measure Theory seminar\n\n\nAbstract\nThis talk will present a cha
 racterisation of purely $n$-unrectifiable subsets $S$ of a complete metric
  space with finite $n$-dimensional Hausdorff measure by studying non-linea
 r projections (i.e. $1$-Lipschitz functions) into some fixed Euclidean spa
 ce. We will show that a typical (in the sense of Baire category) non-linea
 r projection maps $S$ to a set of zero $n$-dimensional Hausdorff measure. 
 Conversely\, a typical non-linear projection maps an $n$-rectifiable subse
 t to a set of positive $n$-dimensional Hausdorff measure. These results pr
 ovide a replacement for the classical Besicovitch–Federer projection the
 orem\, which is known to be false outside of Euclidean spaces.\n\nTime per
 mitting\, we will discuss some recent consequences of this characterisatio
 n.\n
LOCATION:https://researchseminars.org/talk/NCTS-GMT/5/
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