报告题目：On f-polyharmonic maps and submanifolds
时 间：2026年6月30日（星期二）16：30
地 点：知明1-208
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、福建省几何虚拟教研室
参加对象：相关专业师生
报告摘要: This paper initiates the systematic study of $f$-polyharmonic maps of order $k$ (or $f$-$k$-harmonic maps), defined as critical points of the weighted $k$-energy functional $$E_{f,k}(\phi)=\frac{1}{2}\int_M f |\overline{\Delta}^{k/2}\phi|^2 dv_g$$,
where $\overline{\Delta}$ denotes the rough Laplacian on the domain manifold. This framework unifies and significantly extends previous theories including harmonic maps ($k=1$, $f$ constant), $f$-harmonic maps ($k=1$), biharmonic maps ($k=2$, $f$ constant), $f$-biharmonic maps ($k=2$), and polyharmonic maps ($k\geq 3$, $f$ constant). We derive the complete Euler-Lagrange equation for general $f$-polyharmonic maps, revealing a higher-order weighted elliptic system that couples the map with both the curvature of the target and the gradient of the weight function. As concrete applications, we characterize $f$-polyharmonic curves in a general Riemannian manifold $N^n$, and classify $f$-3-harmonic and $f$-4-harmonic curves in a space form $N^2(C)$ that have positive constant geodesic curvature. Furthermore, we provide numerous explicit constructions of proper $f$-polyharmonic functions and maps. We also prove that every $f$-polyharmonic function on a closed Riemannian manifold is constant.
报告人简介：詹鑫，苏州工学院副教授，博士毕业于大连理工大学。主持完成国自然青年科学基金(C类)及江苏省自然青年科学基金各一项，并在《Trans. Amer. Math. Soc.》等期刊上发表过多篇论文。