Alladi Ramakrishnan Hall

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

Akashdeep Dey

Princeton University

Min-max theory for the area functional was developed by Almgren and Pitts to construct closed minimal hypersurfaces in arbitrary closed Riemannian manifolds. There is an alternate PDE based approach 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 Almgren-Pitts min-max theory and the Allen-Cahn min-max theory and discuss the question to what extent these two theories agree.