中科院数学与系统科学研究院

数学研究所

学术报告

几何拓扑研讨班

报告人：谢振肖 副教授(北京航空航天大学）

题  目：Willmore surfaces in 4-dimensional conformal manifolds

时  间：2024.11.05（周二）10:30-11:30

地  点：晨兴 110

摘  要: In this talk, we show the first and second variational formulas of the Willmore functional for closed surfaces in 4-dimensional conformal manifolds. As an application, the Clifford torus in CP^2 is proved to be strictly Willmore-stable. This provides a strong support to the conjecture of Montiel and Urbano, which states that the Clifford torus in CP^2 minimizes the Willmore functional among all tori or all Lagrangian tori. In 4-dimensional locally symmetric spaces, by constructing some holomorphic differentials, we prove that among all minimal 2-spheres only those super-minimal ones can be Willmore. This is a joint work with Prof. Changping Wang.