# The Calabi–Yau Property of Superminimal Surfaces in Self-Dual Einstein Four-Manifolds

@article{Forstneri2020TheCP, title={The Calabi–Yau Property of Superminimal Surfaces in Self-Dual Einstein Four-Manifolds}, author={Franc Forstneri{\vc}}, journal={The Journal of Geometric Analysis}, year={2020}, pages={1-27} }

In this paper, we show that if ( X , g ) is an oriented four-dimensional Einstein manifold which is self-dual or anti-self-dual then superminimal surfaces in X of appropriate spin enjoy the Calabi–Yau property, meaning that every immersed surface of this type from a bordered Riemann surface can be uniformly approximated by complete superminimal surfaces with Jordan boundaries. The proof uses the theory of twistor spaces and the Calabi–Yau property of holomorphic Legendrian curves in complex…

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