Events for 02/16/2023 from all calendars

Noncommutative Geometry Seminar

Time: 09:30AM - 10:30AM

Location: ZOOM

Speaker: Xin Zhou, Cornell

Title: Recent Developments in Constant Mean Curvature Hypersurfaces I

Abstract: We will survey some recent existence theory of closed constant mean curvature hypersurfaces using the min-max method. We hope to discuss some old and new open problems on this topic as well.

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Noncommutative Geometry Seminar

Time: 10:45AM - 11:45AM

Location: ZOOM

Speaker: Liam Mazurowski, Cornell

Title: Recent Developments in Constant Mean Curvature Hypersurfaces II

Abstract: Continuing from the previous talk, we will first discuss two min-max theorems for constructing prescribed mean curvature hypersurfaces in non-compact spaces. The first concerns the existence of prescribed mean curvature hypersurfaces in Euclidean space, and the second concerns the existence of constant mean curvature hypersurfaces in asymptotically flat manifolds. Following this, we will introduce the half-volume spectrum of a manifold M. This is analogous to the usual volume spectrum, except that we restrict to p-sweepouts whose slices are each required to enclose half the volume of M. We use the Allen-Cahn min-max theory to find hypersurfaces associated to the half-volume spectrum. Each hypersurface consists of a constant mean curvature component enclosing half the volume of M plus a (possibly empty) collection of minimal components.

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