- Date de réalisation : 16 Juin 2015
- Durée du programme : 85 min
- Classification Dewey : Mathématiques
- Auteur(s) : Toro Tatiana
- Réalisateur(s) : Bastien Fanny
Dans la même collectionT. Ozuch - Noncollapsed degeneration and desingularization of Einstein 4-manifolds R. Perales - Recent Intrinsic Flat Convergence Theorems R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions A. Mondino - Time-like Ricci curvature bounds via optimal transport D. Semola - Boundary regularity and stability under lower Ricci bounds C. Li - Classifying sufficiently connected PSC manifolds in 4 and 5 dimensions
Tatiana Toro - Geometry of measures and applications (Part 1)
In the 1920's Besicovitch studied
linearly measurable sets in the plane, that is sets with locally finite
"length". The basic question he addressed was whether the infinitesimal
properties of the "length" of a set E in the plane yield geometric
information on E itself. This simple question marks the beginning of the
study of the geometry of measures and the associated field known as
Geometric Measure Theory (GMT).
In this series of lectures we will present some of the main results in the area concerning the regularity of the support of a measure in terms of the behavior of its density or in terms of its tangent structure. We will discuss applications to PDEs, free boundary regularity problem and harmonic analysis. The aim is that the GMT component of the mini-course will be self contained.