We develop an application of Almgren-Pitts min-max theory to the study of minimal hypersurfaces in dimension 3 ≤ m + 1 ≤ 7 as well as computing the k-width of the round 2-sphere for k = 1,...,8. We show that the space of minimal hypersurfaces is non-compact for an analytic metric of positive curvature and construct a min-max unstable closed geodesic in S^2 with multiplicity 2.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:689150 |
| Date | January 2016 |
| Creators | Sarquis Aiex Marini Ferreira, Nicolau |
| Contributors | Neves, André |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/34947 |
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