# PDE Seminar

## Spinor field equations and the problem of prescribing mean curvature on 2-sphere

### 徐甜 博士 (天津大学)

#### 2019年05月10日13:30-14:30 闵行校区数学楼402报告厅

Abstract: In this talk, we shall consider the existence of solutions for the equation $\Delta \psi=Q(x)|\psi|^{\frac2{m-1}}\psi$ on $S^m$, $m\geq2$, where $Q$ is a $C^2$ positive function. We prove that the set of $Q$'s for which a solution exists is dense, in $C^1$-topology, in the space of positive bounded smooth functions. When $m=2$, we relate the zero sets of a solution with the genus of a Riemannian surface. As a consequence, a prescribed mean curvature embedding theorem of 2-sphere into Euclidean 3-space is established.