Talk page

Title:
Min-Max Minimal Hypersurfaces with Higher Multiplicity

Speaker:
Xin Zhou

Abstract:
It is well known that minimal hypersurfaces produced by the Almgren-Pitts min-max theory are counted with integer multiplicities. For bumpy metrics (which form a generic set), the multiplicities are one thanks to the resolution of the Marques-Neves Multiplicity One Conjecture. In this talk, we will exhibit a set of non-bumpy metrics on the standard (n+1)-sphere, in which the min-max varifold associated with the second volume spectrum is a multiplicity two n-sphere. Such non-bumpy metrics form the first set of examples where the min-max theory must produce higher multiplicity minimal hypersurfaces. The talk is based on a joint work with Zhichao Wang (UBC).

Link:
https://www.msri.org/workshops/983/schedules/31120

Workshop:
MSRI- [Virtual] Hot Topics: Regularity Theory for Minimal Surfaces and Mean Curvature Flow