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arXiv · 1804.04243

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

Pedro Gaspar·Marco A. M. Guaraco
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Abstract

We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich-Marques-Neves. As an application we give phase transition adaptations of the proofs of the density and equidistribution of minimal hypersufaces for generic metrics by Irie-Marques-Neves and Marques-Neves-Song, respectively. We also prove the density of separating limit interfaces for generic metrics in dimension 3, based on the recent work of Chodosh-Mantoulidis, and for generic metrics on manifolds containing only separating minimal hypersurfaces, e.g. $H_n(M,\mathbb{Z}_2) = 0$, for $4 \leq n+1 \leq 7$. These provide alternative proofs of Yau's conjecture on the existence of infinitely many minimal hypersurfaces for generic metrics on each setting, using the Allen-Cahn approach.

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Pedro Gaspar, Marco A. M. Guaraco. 2018-04-11. The Weyl Law for the phase transition spectrum and density of limit interfaces. https://arxiv.org/abs/1804.04243

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