主持人：郑宇

报告人简介：洪敏纯，澳大利亚昆士兰大学数学系教授，国际著名几何分析及偏微分方程专家。洪敏纯教授八十年代博士毕业于浙江大学，曾获第一届霍英东青年科学家奖，教育部自然科学一等奖。他在微分几何与非线性分析方面，特别在调和映射、Yang-Mills场、液晶模型偏微分方程等领域做出了杰出贡献，在国际上享有盛誉。在Adv. Math., Math.Ann., J. Funct. Anal.等国际顶尖学术期刊发表论文几十多篇。


报告摘要： In this paper, we establish a parabolic version of the gauge fixing theorem on the Yang-Mills flow and apply it to prove the maximal existence of weak solutions of the Yang-Mills flow in vector bundles over a compact $n$-dimensional manifold with initial value $A_0$ having the curvature $F_{A_0}\in L^{n/2}(M)$ for $n\geq 4$. In particular, we give new proofs on uniform estimates of $\nabla_A^l F_A$ by improving Moser's iterations \cite{Mo1} and an idea of Hamilton \cite{Ha} on the Ricci flow. Furthermore, we investigate the blow-up of the Yang-Mills flow at the maximal existence time $T_1$. Finally, we improve an asymptotical result on the Yang-Mills flow in \cite{HT1}.

(This is a joint work with Jared Casey and Chak Hoi Chan).