UW Analysis, Geometry and Dynamics Seminar: Nick Edelen

Abstract: It's well-known that any holomorphic subvariety is area-minimizing in its homology class.  In this talk we consider the converse question, and we show that any entire area-minimizing 2-surface $M^2 \subset R^n$ of density two at infinity (that is, asymptotic to a pair of planes, possibly coincident) is either planar or is a degree-2 algebraic variety in some $C^2 \subset R^n$.  We additionally prove algebraicity of $M^2$ when the tangent cone at infinity is multiplicity-one.  This is joint work with Luis Atzin Franco Reyna and Paul Minter.