Seminar:
Geometric Analysis and Application
Event time:
Friday, January 21, 2022 - 2:00pm
Speaker:
Zhichao Wang
Speaker affiliation:
University of British Columbia
Event description:
Recently, X. Zhou proved that the Almgren-Pitts min-max solution has multiplicity one for bumpy metrics (Multiplicity One Theorem). In this talk, we exhibit the first set of examples of non-bumpy metrics on the (n+1) -sphere (2≤n≤6 ) in which the varifold associated with the two-parameter min-max construction must be a multiplicity-two minimal n -sphere. This is proved by a new area-and-separation estimate for certain minimal hypersurfaces with Morse index two inspired by an early work of Colding-Minicozzi. This is a joint work with X. Zhou.