On a conjecture of Almgren II: area-minimizing submanifolds with fractal singular sets on almost any manifold

Abstract

This paper is the second in a two-part solution to Almgren's conjecture on the existence of area-minimizing submanifolds with fractal singular sets. In part one, we construct area-minimizing submanifolds with fractal singular sets on certain special manifolds. Here we continue our work and show that area-minimizing submanifolds with fractal singular sets exist on almost any smooth manifold.