Equivariant Allen--Cahn Solutions and the Existence of Cohomogeneity $2$ Minimal Surfaces

Rayssa Caju, Pedro Gaspar, Jared Marx-Kuo

We develop a regularity theory for equivariant Allen--Cahn solutions on closed Riemannian manifolds with a Lie group acting isometrically. When the cohomogeneity of the action is b…