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Geometry-Topology Seminar

Thursday, September 28, 2017 - 4:30pm

Dan Ketover

Princeton University


University of Pennsylvania


The celebrated theorem of Lusternik-Schnirelman states that for any metric on a two-sphere, there are at least three closed embedded geodesics.   The corresponding problem for a Riemannian three-sphere asks to find at least four closed embedded minimal two-spheres.  The existence of at least one two-sphere was obtained by Simon-Smith in 1983.  I’ll explain my joint work with Haslhofer, in which we proved the existence of a second minimal two-sphere.   The proof uses many recent developments in min-max theory and mean curvature flow.  It is also leads to the existence of  minimal non-planar two-spheres in ellipsoids in R^4, answering a question of Yau.