A famous theorem of Simons' states that any minimal hypersurface of the round sphere whose squared second fundamental form is bounded by its dimension, is necessarily a hyperequator. Simons’ methods have been generalized in various directions, in particular to higher codimension minimal immersions. Such results can be improved upon using geometric flows — Baker and Nguyen showed that submanifolds of the sphere satisfying a suitable curvature inequality contract to round points under (high codimension) mean curvature flow.

This seminar will present an algorithm for decomposing immersions satisfying a weaker inequality into a finite number of handles using a surgically modified (high codimension) mean curvature flow.

This is joint work with Lynch and Nguyen.