A comparison of the Almgren-Pitts and the Allen-Cahn min-max theory.

Abstract: Min-max theory for the area functional was developed by Almgren and Pitts to construct closed minimal hypersurfaces in an arbitrary closed Riemannian manifold. There is an alternate approach via PDE to the construction of minimal hypersurfaces. This approach is based on the study of the limiting behaviour of solutions to the Allen-Cahn equation. In my talk, I will briefly describe the Amgren-Pitts min-max theory and the Allen-Cahn min-max theory and discuss the question to what extent these two theories agree.

algebraic topologydifferential geometry

Audience: researchers in the topic

CMI seminar series

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