The Deformation of Lagrangian Minimal Surfaces in KahlerEinstein Surfaces
Abstract
Let $(N,g_{0})$ be a KahlerEinstein 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 KahlerEinstein 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:

arXiv Mathematics eprints
 Pub Date:
 December 1998
 DOI:
 10.48550/arXiv.math/9812081
 arXiv:
 arXiv:math/9812081
 Bibcode:
 1998math.....12081L
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Symplectic Geometry
 EPrint:
 LaTeX, 29 pages, to appear in JDG