On Doubling Constructions for Minimal Surfaces

On Doubling Constructions for Minimal Surfaces

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Peter McGrath, University of Pennsylvania
Fine Hall 314

I will discuss recent and ongoing work (with Nikolaos Kapouleas) on constructions of new embedded minimal surfaces using singular perturbation gluing methods.  I will discuss at length doublings of the equatorial $S^2$ in $\S^3$.  In contrast to earlier work of Kapouleas, the catenoidal bridges  may be placed on arbitrarily many parallel circles on the base $S^2$, with the option to include the poles.  This necessitates a detailed understanding of the linearized problem and more exacting estimates on associated linearized doubling solutions.