Thu, November 20, 2025
3:00 pm - 3:55 pm
Scott Labs E001
Xin Zhou
Cornell University
Title
Volume Spectrum, minimal and constant mean curvature surfaces
Abstract
The volume spectrum is an analogue of the Laplace spectrum, defined through the area functional together with homological or cohomological relations in the space of hypercycles. In this talk, I will introduce several versions of the volume spectrum and highlight its applications in geometric variational theory. Specifically, I will discuss how the spectrum can be used to address existence problems for minimal surfaces and constant mean curvature surfaces. Finally, I will present recent progress on extending these ideas to a higher codimensional problem.