Speaker
Description
Besicovitch's problem
Besicovitch's problem investigates the smallest threshold guaranteeing rectifiability for a set with Hausdorff -dimensional finite measure when the lower density of the set is larger than almost everywhere. Besicovitch conjectured that (hence the name of the problem) and proved , then Preiss and Tišer improved the bound to . In a recent work in collaboration with C. De Lellis, F. Glaudo and D. Vittone, we devise a strategy to improve the bound by means of a hierarchy of variational problems and we reach a proof that . In this seminar, I will try to explain the fairly intuitive geometric idea behind this strategy and I will try to summarize both the computational obstacles and the intrinsic obstacles that are still in the way.
