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Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary

Martin Man-chun Li Chinese University of Hong Kong Ailana Fraser University of British Columbia

Differential Geometry Geometric Analysis and Geometric Topology mathscidoc:2001.10001

Journal of Differential Geometry, 96, (2), 183-200, 2014
We prove a lower bound for the first Steklov eigenvalue of embedded minimal hypersurfaces with free boundary in a compact n-dimensional Riemannian manifold which has nonnegative Ricci curvature and strictly convex boundary. When n=3, this implies an apriori curvature estimate for these minimal surfaces in terms of the geometry of the ambient manifold and the topology of the minimal surface. An important consequence of the estimate is a smooth compactness theorem for embedded minimal surfaces with free boundary when the topological type of these minimal surfaces is fixed.
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@inproceedings{martin2014compactness,
  title={Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary},
  author={Martin Man-chun Li, and Ailana Fraser},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200103162445003232615},
  booktitle={Journal of Differential Geometry},
  volume={96},
  number={2},
  pages={183-200},
  year={2014},
}
Martin Man-chun Li, and Ailana Fraser. Compactness of the space of embedded minimal surfaces with free boundary in three-manifolds with nonnegative Ricci curvature and convex boundary. 2014. Vol. 96. In Journal of Differential Geometry. pp.183-200. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20200103162445003232615.
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