Time：15:00-16:00, Monday, October 27 2025
Venue：E10-201
Host：Xujia Wang, ITS
Speaker：Richard Schoen, University of California, Irvine
Biography：Richard Schoen, a distinguished professor at UC Irvine and a world leader in differential geometry and mathematical physics, is celebrated for a series of profound breakthroughs that have fundamentally advanced these fields. His celebrated contributions include the proof of the positive mass theorem, the complete resolution of the Yamabe problem, the proof of the differentiable sphere theorem, and groundbreaking work on harmonic maps. His exceptional career has been recognized with numerous honours, including a Sloan Fellowship (1979), a MacArthur Fellowship (1983), and invitations to speak at the International Congress of Mathematicians three times, twice as a Plenary Speaker. He was elected to the National Academy of Sciences in 1991 and is a recipient of the Bôcher Memorial Prize (1989), the Wolf Prize (2017), and the WLA Prize in Mathematics (2025).
Title：Minimal surfaces defined by extremal eigenvalue problems
Abstract: Minimal surfaces in spheres are characterized by the condition that their embedding functions are eigenfunctions on the surface with its induced metric. The metric on the surface turns out to be an extremal for the eigenvalue among metrics on the surface with the same area. In recent decades, this extremal property has been used to construct new minimal surfaces by eigenvalue maximization. There is an analogous theory for minimal surfaces in the euclidean ball with a free boundary condition. In this talk we will describe new work that generalizes this idea to products of balls. We will describe the general theory and apply it in a specific case to explain and generalize the Schwarz p-surface, which is a free boundary minimal surface in the three dimensional cube with one boundary component on each face of the cube. We will show how the method can be used to construct such surfaces in rectangular prisms with arbitrary side lengths.
