学术报告（黄少创 11.16）

In this talk, we will talk about a short time existence result for harmonic map heat flow coupled with a smooth family of complete metrics in the domain manifold. This result generalizes short time existence results for harmonic map heat flow by Li-Tam and Chen-Zhu. In particular, we prove the short time existence of harmonic map heat flow along a complete Ricci flow g(t) on M into a complete manifold with curvature bounded from above with a smooth initial map of uniformly bounded energy density, under the assumptions that |Rm(g(t))| ≤ a/t and g(t) is uniformly equivalent to g(0). The main motivation of this work is the uniqueness problem of Ricci flow. This is a work joint with Luen-Fai Tam.