Minimal surfaces and deformations of holomorphic curves in Kähler-Einstein manifolds. (English) Zbl 1010.58006
The author gives explicit examples of stable nonholomorphic minimal surfaces representing classes of type (1,1) in Kähler-Einstein 4-manifolds of negative scalar curvature. He uses the implicit function theorem for the area functional to deform some holomorphic rational curves as minimal surfaces to nearby Kähler-Einstein metric; then by some results in the theory of deformations of Hodge structure, he can prove that the generic of these deformations cannot be holomorphic in the deformed complex structure.
Reviewer: Chen Qing (Anhui)
MSC:
| 58E12 | Variational problems concerning minimal surfaces (problems in two independent variables) |
| 53A10 | Minimal surfaces in differential geometry, surfaces with prescribed mean curvature |
| 58C15 | Implicit function theorems; global Newton methods on manifolds |
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