The sharp L²-Michael-Simon-Sobolev inequality via conformal geometry

We use methods from conformal geometry to show that the best constant in the $L^2$-Michael-Simon-Sobolev inequality for an n-dimensional minimal submanifold of Euclidean $N$-space is equal to the sharp constant in the usual $L^2$-Sobolev inequality on ${\mathbb{R}}^n$ as computed by Aubin and Talenti. This removes the codimension restriction $N\le n+2$ from a result of Brendle. This is joint work with Jeffrey Case. https://www.kaltura.com/tiny/423y4a97