The Deformation of Lagrangian Minimal Surfaces in Kahler-Einstein Surfaces

1998/12/14 by Yng-Ing Lee, Lee, Yng-Ing
Mathematics · #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Symplectic Geometry (math.SG) #math.DG #math.SG

paper · pdf · doi:10.48550/arxiv.math/9812081

LaTeX, 29 pages, to appear in JDG

arxiv created 1998/12/14 · openalex publication_date 1998/12/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (N,g₀) be a Kahler-Einstein surface with the first Chern class negative and assume that there exists a branched Lagrangian minimal surfaces with respect to the metric g₀. We show that when the Kahler-Einstein metric is changed in the same component (i.e. the complex structure is changed), the Lagrangian minimal surface can be deformed accordingly. To get the result, we first obtain a theorem on the deformation of the branched minimal surfaces in a complete Riemannian n-manifold and also generalize a result of J. Chen and G. Tian on the limit of adjunction numbers.

Citations

• Existence of Incompressible Minimal Surfaces and the Topology of Three Dimensional Manifolds with Non-Negative Scalar Curvature
• Calibrated geometries

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