Low min-max widths of the round three-sphere
Charles Arthur George Nurser · 2016
Almgren-Pitts min-max theory considers the space of integral currents on a manifold with the associated mass functional. Minimal hypersurfaces arise as the critical points of the mass functional, and so can be constructed using min-max techniques applied to certain families of integral currents. A particular set of families is the Gromov-Guth p-sweepouts. The min-max masses associated with these families are the p-widths. This thesis calculates several p-widths for p 1, index <= 9 and area equal to the 9-width.