Talk
On Minimality of Determinantal Varieties
- Khazhgali Kozhasov (Technical University Braunschweig)
Abstract
Minimal submanifolds are mathematical abstractions of soap films: they minimize the Riemannian volume locally around every point. Finding minimal algebraic hypersurfaces in $R^n$ for each n is a long-standing open problem posed by Hsiang. In 2010 Tkachev gave a partial solution to this problem showing that the hypersurface of n x n real matrices of corank one is minimal. I will discuss the following generalization of this fact to all determinantal matrix varieties: for any m, n and r<m,n the (open) variety of m x n real matrices of rank r is minimal.</p>
