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##### Department of Mathematics, University of California San Diego

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## A nonlinear spectrum on closed manifolds

##### Abstract:

The p-widths of a closed Riemannian manifold are a nonlinear analog of the spectrum of its Laplace--Beltrami operator, which was defined by Gromov in the 1980s and correspond to areas of a certain min-max sequence of hypersurfaces. By a recent theorem of Liokumovich--Marques--Neves, the p-widths obey a Weyl law, just like eigenvalues do. However, even though eigenvalues are explicitly computable for many manifolds, there had previously not been any ≥ 2-dimensional manifold for which all the p-widths are known. In recent joint work with Otis Chodosh, we found all p-widths on the round 2-sphere and thus the previously unknown Liokumovich--Marques--Neves Weyl law constant in dimension 2.

Host: Luca Spolaor

### AP&M 5218

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