Multiplicity one of generic stable Allen-Cahn minimal hypersurfaces
Marco Guaraco (Imperial)
Abstract: Allen-Cahn (AC) minimal hypersurfaces are limits of nodal sets of solutions to the AC equation. An important problem is to understand the local picture of this convergence. For instance, can we avoid the situation in which the nodal set looks like a multigraph over the limit hypersurface? General examples of this phenomenon, known as “multiplicity” or "interface foliation”, exist when the limit hypersurface is unstable. Together with A. Neves and F. Marques we proved that, generically and in all dimensions, these are the only possible examples of interface foliation, i.e. generic stable AC minimal hypersurfaces can only occur with multiplicity one. We will discuss this and other topics.
differential geometry
Audience: researchers in the topic
Organizers: | Joel Fine, Lorenzo Foscolo*, Peter Topping |
Curators: | Jason D Lotay*, Costante Bellettini, Bruno Premoselli, Felix Schulze, Huy The Nguyen, Marco Guaraco, Michael Singer |
*contact for this listing |