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The p-widths of a surface

Mathematical Physics Seminar

Speaker: Otis Chodosh, Stanford
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Location: 3204 QMAP
Start time: Mon, Oct 2 2023, 3:10PM

This concerns joint work with Christos Mantoulidis. I will discuss a nonlinear version of the spectrum of the Laplacian introduced by Gromov (the p-widths) where "eigenfunction" is replaced by "minimal hypersurface." The p-widths satisfy a Weyl law and other nice properties (and have been used to prove various conjectures about minimal surfaces). However, (in contrast with the Laplacian) there's only one manifold whose p-widths are completely known: the round 2-sphere. I will explain the special issues that arise in 2-dimensions as well as how their resolution can be used to compute the p-widths of the 2-sphere.