2017/01/25 by Hui Ma, Ma, Hui, Andrey E. Mironov +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1701.07211
openalex publication_date 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study Lagrangian tori in \mathbb CP2. A two-dimensional periodic Schrödinger operator is associated with every Lagrangian torus in \mathbb CP2. We introduce an energy functional for tori as an integral of the potential of the Schrödinger operators, which has a natural geometrical meaning. We study the energy functional on two families of Lagrangian tori and propose a conjecture that the minimum of the functional is achieved by the Clifford torus. We also study deformations of minimal Lagrangian tori. In particular we show that if the deformation preserves a conformal type of the torus, then it also preserves the area of the torus. Thus it follows that deformations generated by Novikov-Veselov equations preserve the area of minimal Lagrangian tori.