Index, multiplicity, and curvature estimates for Allen--Cahn min-max in 3-manifolds

Otis Chodosh, Princeton University
Fine Hall 1201

: The Allen--Cahn equation is a semi-linear PDE that produces minimal surfaces via a certain singular limit. We will describe recent work proving index, multiplicity, and curvature estimates in the context of an Allen--Cahn min-max construction in a 3-manifold. Our results imply, for example, that in a 3-manifold with a generic metric, for every positive integer p, there is an embedded, two-sided minimal surface of Morse index p. This is joint with Christos Mantoulidis.