西南大学数学与统计学院

报告题目：Quantitative stratification for the singular set of the approximate biharmonic maps.

报告人：郑高峰，华中师范大学

报告时间：2023年10月12日（星期四）上午9：00-10：00

报告地点：数学大楼914

摘要：In this talk, we are concerned with the stationary approximate biharmonic maps. Using the gauge transformation method, we obtain the epsilon regularity of the approximate biharmonic maps. As a result, we get the H\"{o}lder continuity of the solution except for a set of Hausdorff dimension at most $m-4$. With the help of regularity, we obtain the compactness for $f$-minimizing or stationary biharmonic maps under additional condition. This compactness, together with the monotonicity, enable us to use the dimension reduction method to show the Hausdorff dimension of an $f$- minimizing biharmonic map is at most $m-5,$ and can be reduced further for certain target manifold. Using Naber-Valtorta's techniques,  a Minkowski content bound and rectifiability for strata of hte singular set of an $f$-stationary biharmonic map are established. This a a jointed work with Chang-Yu Guo, Gui-Chun Jiang, and Chang-Lin Xiang. Chang-Yu Guo, Gui-Chun Jiang, and Chang-Lin Xiang

报告人简介：郑高峰，华中师范大学教授，博士生导师。2005年毕业于香港中文大学，获博士学位。主要从事偏微分方程的研究工作。主持国家自然科学基金5项、留学基金委留学回国人员项目1项。曾在德国柏林自由大学（洪堡学者）、美国普渡大学、中佛罗里达大学、澳大利亚国立大学、芬兰于韦斯屈莱大学等访问。在J.Math. Pure Appl.,JFA, Calculus of Variation and PDEs, Ann. I. H. Poincare-AN,JDE等杂志上发表SCI论文二十余篇。作为主要成员获得国家高等学校教学成果奖二等奖1项，湖北省教学成果特等奖1项、一等奖2项。