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February 1, 2019

  

Friday, February 01, 2019

Quantitative Radon-Nikodym in Hilbert spaces.
3:30 PM - 4:30 PM

Speaker. Thierry De Pauw (East China Normal University, Shanghai)

Abstract. This lecture will review the case of an ambient inner product space. If A is a Borel subset of Euclidean space such that the measure H^m L A is Radon, then A is m rectifiable if and only is its tangent measures are m flat almost everywhere, if and only if H^m L A has density 1 a.e., according to P. Mattila. In a Hilbert space we establish links between the growth of H^m L A in balls and A being regular, i.e. a Holder continuously differentiable submanifolds. This study is based on moments computations, after D. Preiss, adapted to an infinite dimensional setting. We next show how this applies to proving partial regularity of (almost) mass minimising G chains in Hilbert space, adapting E.R. Reifenberg’s epiperimetric inequality. This is joint work with R. Zuest.

The lecture will be held in Krieger 300.

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