Recently, X. Zhou proved the multiplicity one theorem for bumpy metrics in the Almgren-Pitts theory. This made it tempting to conjecture that for any metric there always exists a min-max varifold of multiplicity one.  However, in this talk, we will disprove this naive conjecture by constructing the first set of nontrivial and non-bumpy examples, where the varifold associated with a two-parameter min-max construction must have multiplicity two. This is a joint work with X. Zhou.

Speaker：

Zhichao Wang 

Zhichao Wang is currently a postdoc at the University of British Columbia. He obtained his bachelor from Nankai University in 2013 and received Ph.D. in 2018 from BICMR in Peking University under the supervision of Prof. Gang Tian. His research focuses on geometric variational problems, particularly the existence and geometric property of minimal submanifolds Riemannian manifolds. The basic tools are Almgren-Pitts min-max theory and mean curvature flow.

Zoom:

https://us02web.zoom.us/j/83867407785?pwd=TXcyTjJiSk5zRnFoVHhsK213U2lYQT09

ID: 838 6740 7785

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