理学院数理讲坛（2018年第05讲）
报告题目：An Energy functional for Lagrangian tori in CP^2
报告人：左达峰教授，博导
单 位：中国科学技术大学数学院
报告时间：2018年1月12日 上午 9:30-10:30
报告地点：阳明学院楼（包玉书9号楼） 303
报告摘要：A two-dimensional periodic Schr\"{o}dingier operator is associated with every Lagrangian torus in the complex projective plane ${\mathbb C}P^2$. Using this operator we introduce an energy functional on the set of Lagrangian tori. It turns out this energy functional coincides with the Willmore functional $W^{-}$ introduced by Montiel and Urbano. We study the energy functional on a family of Hamiltonian-minimal Lagrangian tori and support the Montiel--Urbano conjecture that the minimum of the functional is achieved by the Clifford torus. We also study deformations of minimal Lagrangian tori and show that if a deformation preserves the conformal type of the torus, then it also preserves the area, i.e. preserves the value of the energy functional. In particular, the deformations generated by Novikov—Veselov equations preserve the area of minimal Lagrangian tori. This is a joint work with Hui Ma and Andrey E.Mironov.