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Explore free boundary minimal annuli immersed in the 3-ball in this 55-minute seminar talk by Peter McGrath from North Carolina State University. Delve into a recent construction developed with N. Kapouleas, focusing on immersed free boundary minimal annuli in the unit 3-ball. Learn about the singular perturbation PDE methods used to create these surfaces by "doubling" an equatorial halfdisk, resulting in arbitrarily small first Steklov eigenvalue. Examine topics such as free boundary minimal submanifolds, uniqueness for the critical catenoid, the Steklov eigenvalue problem, eigenvalue and area bounds, the Jacobi equation, and the process of perturbing to exact free boundary minimality. Gain insights into constructing initial surfaces and the implications of this research in the field of spectral geometry.
