Introduction to GMT -- Varifolds and the Allard regularity theorem


天數 102


2017-05-02 (星期二) 16:30 - 18:30


A "rectifiable $n$-varifold" is an equivalent class of $H^n$-measurable $n$-rectifiable sets. That is, the objects discussed in the last theorem. I will state the Allard regularity theorem, which says that under some conditions, a varifold which is nearly minimal is always a $C^{1,\alpha}$ submanifold. And then I will try to talk as much as possible about its proof.


  1. L. Simon, Lecture on Geometric Measure Theory.
  2. R. Hardt & L. Simon, Seminar on Geometric Measure Theory.