浙大-西湖几何分析讨论班—Existence of four minimal spheres in S^3 with a bumpy metric

Abstract:

In this talk, we show that in the three dimensional sphere with a bumpy metric or a metric with positive Ricci curvature, there exist at least four distinct embedded minimal two-spheres. This confirms a conjecture of S. T. Yau in 1982 for bumpy metrics and metrics with positive Ricci curvature. The proof relies on a multiplicity one theorem for the Simon-Smith min-max theory. This is a joint work with Xin Zhou.