Graduate Student / Postdoc Seminar
Fine structure of measures satisfying a PDE constraint
Speaker: Guido De Philippis, CIMS
Location: Warren Weaver Hall 1302
Date: Friday, December 6, 2019, 1 p.m.
In this talk I will present some new result concerning the structure of measure satisfying a linear PDE constraint. In 2016, in collaboration with Filip Rindler, we prove a first structural result concerning the singular part of measure subject to PDE constraint. This turned out to have several applications in GMT and in Geometric Analysis.
In a later work joint with Adolfo Arroyo Rabasa, Jonas Hirsch and Filip Rindler we improve upon this result proving a more precise structure on the “low” dimensional part of the measure. As a corollary we recover several known rectifiability results.
In this talk I will try to give an overview of both these results, of their applications and I will present some new open problems and new lines of research.