The Deformation of Lagrangian Minimal Surfaces in Kahler-Einstein Surfaces
Abstract
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.
- Publication:
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arXiv Mathematics e-prints
- Pub Date:
- December 1998
- DOI:
- 10.48550/arXiv.math/9812081
- arXiv:
- arXiv:math/9812081
- Bibcode:
- 1998math.....12081L
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Symplectic Geometry
- E-Print:
- LaTeX, 29 pages, to appear in JDG