Università degli Studi di Padova

“Rectifiability of stationary varifolds branching set with multiplicity at most 2”

Martedì 23 Gennaio 2024, ore 17:00 - Aula 2AB40 - Paolo De Donato (Università degli Studi di Padova)


Almgren introduced for the first time the frequency function to prove that the singular set of so-called Dir-minimizing Q-valued functions on $R^n$ has Hausdorff dimension at most n-2. This frequency function then played a fundamental role for estimating the Hausdorff dimension of mass-minimizing currents, and many variants of the frequency function have been developed by many authors to study regularity properties of some classes of varifolds and currents. In this talk I give a brief outline of Almgren’s proof about the estimate of the Hausdorff dimension of the singular set of Dir-minimizing functions and how these techniques can be adapted to study rectifiability of the singular set of some varifolds with arbitrary codimension.

Mathematics in Conversation