Larguras min-max baixas do espaço projetivo real RP3

Abstract

Minimal hypersurfaces appear as critical points of the mass functional, and therefore can be produced by min-max techniques applied to certain families of currents. A particular set of such families are p-sweepouts, where p-widths are the min-max invariant associate. In this thesis, we deal with the min-max invariant known as 1-width. For this proposal, we have used the Marques’ and Neves’ idea to compute the 1-width of the real projective space RP3, more specifically, using the ideas in [12] we are able to compute the 1-width using a abstract 1-sweepout. Moreover, we present an explicite sharp 1-sweepout. Next, we compute the second width of the 3-dimensional projective space using an explicite sweepout to get a sharp upper bound, and finally we also estimate the 9-width.