Abstract: We will discuss the shape of the min-max minimal hypersurface produced by Almgren and Pitts corresponding to the fundamental class of a Riemannian manifold of positive Ricci curvature. We will give a characterization of the Morse index, area and multiplicity. The min-max minimal hypersurface will have a singular set of codimension 7, and the talk will give new ideas to deal with the singularity issue.

Time: 10:10am-12:00pm, Tuesday, Jan. 09

Place: Room 29, Quan Zhai, BICMR

Speaker: ZHOU Xin, MIT