Multiplicity one of generic stable Allen-Cahn minimal hypersurfaces

Geometry & Topology
Event time: 
Tuesday, March 30, 2021 - 4:00pm
Marco Méndez Guaraco
Speaker affiliation: 
Imperial College London
Event description: 

"Allen-Cahn minimal hypersurfaces” are obtained as limits of nodal sets of solutions to the Allen-Cahn equation. Understanding the local picture of this convergence is a fundamental problem. For instance, can we avoid the situation of a nodal set looking like a multigraph over the limit hypersurface? Examples of this phenomenon, called “multiplicity” or "interface foliation”, are known when the limit hypersurface is unstable. Together with A. Neves and F. Marques we proved that generically (and in all dimensions) stable Allen-Cahn minimal hypersurfaces can only occur with multiplicity one. We will discuss this and other topics.

Special note: 
Email Franco or Caglar for password.