Abstract: 

In this presentation, we talk about the stability of the Willmore functional. For an integral 2-varifold in with square integrable gene ralized mean curvature and finite mass, if its Willmore energy is smaller than   and the mass is normalized to be, we show that is and bi-Lipschitz close to the standard embedding of the round sphere in a quantitative way when For, we prove that the sharp constant is. This is a joint work with Dr. Yuchen Bi.