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Geometric Analysis Seminar

Minimal surfaces in geometry and topology 

Daniel Ketover (Princeton University)

Location:  Hill 705
Date & time: Tuesday, 20 February 2018 at 2:45PM - 3:45PM

Abstract: Minimal surfaces are critical points of the area functional and have been studied since the 1700s, but they are hard to construct.  In the 80s Simon and Smith developed a theory to construct them in great generality in closed 3-manifolds.  However, a key missing piece in their work was controlling the topological type of the surfaces one produces.  I’ll describe several new instances in which we can control the topological type and how one can then use such minimal surfaces to solve problems in three-manifold topology.   I’ll then turn to the problem of constructing minimal spheres in Riemannian three-spheres and show how the variational theory leads to an answer of a problem of Yau on the existence of non-planar minimal two-spheres in ellipsoids in R^4. 

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