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Friday, June 10, 2022
1:00 PM - 2:00 PM
Linde Hall 187

Geometry and Topology Seminar

On Steklov Eigenspaces for Free Boundary Minimal Surfaces
Peter McGrath, Department of Mathematics, North Carolina State University,

It has been conjectured that the first nontrivial eigenvalue of the Dirichlet-to-Neumann map on an embedded free boundary minimal surface in the unit 3-ball is one. I will discuss recent work with R. Kusner which provides sufficient criteria for the first eigenvalue on such a surface to be equal to one, and moreover that the corresponding eigenspace is spanned by the coordinate functions. A consequence of this work is that an embedded antipodally invariant free boundary minimal annulus in the unit ball is congruent to the critical catenoid.

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