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M. E. Taylor Analysis and PDE Seminar – Peter McGrath (NCSU)

February 7 @ 3:30 pm - 4:30 pm

Eigenvalue Optimization and Minimal Surfaces

Abstract. I will discuss a new method, developed in collaboration with M. Karpukhin, R. Kusner, and D. Stern, for constructing minimal surfaces embedded in the 3-sphere and the 3-ball, by equivariant eigenvalue optimization. A main application is that each topological type of compact oriented surface is realized as a minimal surface with free boundary in the 3-ball, resolving a question of Fraser-Li. More generally, we prove the number of such surfaces with a given genus and number of boundary components grows linearly with the genus, provided the number of boundary components is at least two.

M. E. Taylor Analysis and PDE Seminar Website


February 7
3:30 pm - 4:30 pm
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