题目：Quantitative stratification for the singular set of the approximate biharmonic maps
报告人：郑高峰 教授 华中师范大学
邀请人：李沁峰
时间：2023-9-15 3:30-4:30
地点：数学院425报告厅
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.
报告人简介：郑高峰教授，现任华中师范大学数学与统计学学院教学副院长。主要从事偏微分方程、几何发展方程、几何测度论的研究。曾作为成员获国家教学成果奖二等奖一项、湖北省教学成果奖一等奖两项，获华中师范大学第七届“桂苑名师”称号。曾主持国家自然科学基金面上项目、青年基金、天元基金和留学回国人员启动基金项目，并作为主要成员参加过多项国家自然科学基金项目的研究。在J. Math. Pures Appl.，J. Func. Anal.，Ann. Inst. H. Poincaré Anal. Non Linéaire，J. Differential Equations，Calc. Var. Partial Differential Equations等国际著名杂志上发表学术论文多篇。
