广州数学大讲坛第十一期

第一百零七讲——华中师范大学郑高峰教授学术报告


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

时间:2023年12月2日(星期六)14:00-15:30

地点:腾讯会议(会议ID:576-512-879)

报告人:郑高峰教授

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.