Geometric Analysis and Topology Seminar

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Half-volume Spectrum and Constant Mean Curvature Hypersurfaces

Speaker: Xin Zhou, Cornell University

Location: Warren Weaver Hall 512

Date: Friday, March 7, 2025, 11 a.m.

Synopsis:

We will introduce the half-volume spectrum, a new variational invariant inspired by the classical volume spectrum, but defined by considering only hypersurfaces that divide the ambient manifold into equal volumes. We will present a new min-max theory for constant mean curvature (CMC) hypersurfaces specifically associated with the half-volume spectrum. As an application, we establish a CMC analogue of Yau’s abundance conjecture and show that it holds generically in low dimensions. This is based on joint work with Liam Mazurowski.