Currents and Flat Chains Associated to Varifolds, with an Application to Mean Curvature Flow

We prove under suitable hypotheses that convergence of integral varifolds implies convergence of associated mod 2 flat chains and subsequential convergence of associated integer-multiplicity rectifiable currents. The convergence results imply restrictions on the kinds of singularities that can occur in mean curvature flow.Comment: 16 pages. Revised to correct one typo (in equation (12)

Lectures on Minimal Surface Theory

An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.Comment: 46 pages, 6 figures. Some references added/corrected on August 2, 2014. A few minor corrections on October 16, 2015. Additional typos corrected on January 17, 201

Rectifiability of flat chains

We prove (without using Federer's structure theorem) that a finite-mass flat chain over any coefficient group is rectifiable if and only if almost all of its 0-dimensional slices are rectifiable. This implies that every flat chain of finite mass and finite size is rectifiable. It also leads to a simple necessary and sufficient condition on the coefficient group in order for every finite-mass flat chain to be rectifiable.Comment: 20 pages, published versio