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Title: Low min-max widths of the round three-sphere
Author: Nurser, Charles Arthur George
ISNI:       0000 0004 7233 1394
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2016
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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 <= 13 in the case of the round three-sphere by explicit construction of p-sweepouts and Lusternik-Schnirelmann topological arguments. It follows from recent developments in min-max theory that there is a minimal surface with genus > 1, index <= 9 and area equal to the 9-width.
Supervisor: Neves, Andre Sponsor: Engineering and Physical Sciences Research Council
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral