Geometry/topology Seminar
Monday, October 25, 2021, 3:15pm, Zoom link
Lucas Ambrozio (IMPA, Mathematics)
Some interesting metrics related to isoperimetric-like inequalities for least area minimal two-spheres in three-spheres
Abstract:
Simon and Smith constructed an embedded minimal bi-dimensional sphere on every Riemannian three-dimensional sphere. A few interesting geometric invariants of Riemannian three-spheres can be defined as a consequence of their construction, for example the first spherical min-max width or the infimum of the area of such minimal two-spheres. In a joint work with Rafael Montezuma (UFC), we investigated upper bounds for these quantities among metrics that have the same volume. Among other things, that work was suggestive of the existence of a large class of metrics admitting "the maximal number" of minimal two-spheres. In this talk, we will discuss this curious circle of ideas, and present some new existence and classification results that we obtained, during the last three years, in collaboration with Fernando Coda Marques (Princeton) and Andre Neves (Chicago).

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