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We prove under suitable hypotheses that convergence of integral varifoldsimplies convergence of associated mod 2 flat chains and subsequentialconvergence of associated integer-multiplicity rectifiable currents. Theconvergence results imply restrictions on the kinds of singularities that canoccur in mean curvature flow.

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