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The Allen-Cahn construction of minimal hypersurfaces
If you have a question about this talk, please contact cbz20.
The existence of embedded minimal hypersurfaces is a question that eluded geometric analysts for the better part of the twentieth century; it was eventually settled in 1981 via the so-called Almgren-Pitts construction. This construction on min-max arguments for a suitably enlarged space of hypersurfaces, and relies on machinery from geometric measure theory.
My talk will instead focus on a more recent approach to the problem, where one constructs minimal hypersurfaces that arise from the level sets of solutions to an elliptic PDE , called the Allen-Cahn equation. I will present an overview of this theory that requires no prior knowledge of geometric analysis.
This talk is part of the Junior Geometry Seminar series.
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