# The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature

@article{Choi1985TheSO, title={The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature}, author={Hyeong In Choi and Richard M. Schoen}, journal={Inventiones mathematicae}, year={1985}, volume={81}, pages={387-394} }

In this paper we obtain a curvature estimate for embedded minimal surfaces in a three-dimensional manifold of positive Ricci curvature in terms of the geometry of the ambient manifold and the genus of the minimal surface. It should be mentioned that there are two main points in our result: One is the absence of a stability assumption and the other is the requirement of being embedded. Most known curvature estimates require the stability assumption, and once the stability assumption is dropped… Expand

#### 191 Citations

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