University of Cambridge > Talks.cam > Geometric Analysis and Partial Differential Equations seminar > Min-max, phase transitions and minimal hypersurfaces.

Min-max, phase transitions and minimal hypersurfaces.

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If you have a question about this talk, please contact Harsha Hutridurga.

We present a new min-max method for constructing embedded minimal hypersurfaces in an arbitrary closed manifold of any dimension. Our approach is variational, but it is substantially different from Almgren-Pitts theory since it is based on the strong correspondence between the theory of phase transitions and the theory of minimal hypersurfaces. As a preliminary, we use ideas of Pitts to extend to the case of critical points of any index, recent results of Tonegawa-Wickramasekera for stable phase transitions. We also study the correspondence of critical points between both theories from a “global” variational point of view in the case of those obtained by min-max. In particular, we compare our construction of a minimal hypersurface with that of Almgren-Pitts and its refinement by Simon-Smith in dimension 3.

This talk is part of the Geometric Analysis and Partial Differential Equations seminar series.

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