Weyl Law for the phase transition spectrum and density of limit-interfaces

Marco Mendez Guaraco
Member, School of Mathematics
November 5, 2018

Abstract: The Allen-Cahn equation behaves as a desingularization of the area functional.  This allows for a PDE approach to the construction of minimal hypersurfaces in closed Riemannian manifolds. After presenting and overview of the subject, I will discuss recent results regarding a Weyl Law and its consequences for the density of minimal hypersurfaces in generic metrics. This is joint work with P. Gaspar.