摘要：In this talk，we'll consider the  non-negative scalar curvature (NNSC) fill-in and cobordism problem and mainly give some non existence results.  Roughly speaking, for the Bartnik data $(\Sigma^{n-1}, \gamma, H)$, suppose $\Sigma^{n-1}$ is the topological sphere $S^{n-1}$, $\gamma$ is a positive scalar cuvature metric and $3\le n\le 7$, then $(\Sigma^{n-1}, \gamma, H)$ admit no NNSC fill-in provided the mean curvature $H$ is sufficiently large.  Similaly, for Bartnik data $(\Sigma_i^{n-1}, \gamma_i, H_i)$, $i=1,2$, suppose each $\Sigma_i^{n-1}$ is the topological sphere $S^{n-1}$,  each $\gamma_i$ is a positive scalar cuvature metric, $3\le n\le 7$ and $H_1$ is fixed, then they adimit no  NNSC cobordism provided the mean curvature $H_2$ is sufficiently large.

联系人：王枫wfmath@zju.edu.cn