The Deformation of Lagrangian Minimal Surfaces in Kahler-Einstein Surfaces

Details The Deformation of Lagrangian Minimal Surfaces in Kahler-Einstein Surfaces The Deformation of Lagrangian Minimal Surfaces in Kahler-Einstein Surfaces

1998-12-14

arxiv.org/abs/math/9812081v1

Mathematics

Differential Geometry

LaTeX, 29 pages, to appear in JDG

Scientific paper

Let $(N,g_{0})$ 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 $g_{0}$. 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.

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