报告题目：The Willmore Problem for Surfaces in R^3 and R^4
时 间：2026年1月20日(星期二) 下午15：00
地 点：科研楼18号楼1101
主 办：数学与统计学院，分析数学及应用教育部重点实验室，分析数学及应用福建省重点实验室
参加对象：相关专业师生
报告摘要：Consider the “Willmore Problem” of minimizing --- or finding stationary surfaces for --- the scale-invariant “bending energy” W(M) := \int_M H^2 dA among surfaces in R^n of fixed topological type. Besides the intrinsic topology of M, its extrinsic topology --- i.e., the path component of M in the space of immersed surfaces in R^n of given regular boundary type --- should also be taken into account.We will offer a working guide to these classes for n = 3 and 4, the only dimensions we use are those of immersed surfaces with distinct regular boundary classes, though the “higher” extrinsic topology in the space of immersed surfaces for n > 4 is nontrivial and may be useful for understanding unstable W-stationary surfaces; We also survey what is known regarding the existence of W-minimizers and infimal values for each regular boundary class.
报告人简介：Rob Kusner，美国麻省大学阿默斯特分校教授，主要从事几何变分问题及低维拓扑研究，相关论文发表于Invent Math., GAFA, JDG, Amer J. Math., J. Reine Angew. Math., Geometry & Topology, Arch. Rat. Mech. Anal., Nature, PNAS等国际重要学术期刊.