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Existence of minimal surfaces of arbitrary large Morse index

Haozhao L University of Science and Technology of China, Xin Zhou Massachusetts Institute of Technology

Differential Geometry mathscidoc:1610.10030

Distinguished Paper Award in 2017

Calculus of Variations and Partial Differential Equations, 55, (64), 2016.6
We show that in a closed 3-manifold with a generic metric of positive Ricci curvature, there are minimal surfaces of arbitrary large Morse index, which partially confirms a conjecture by Marques and Neves. We prove this by analyzing the lamination structure of the limit of minimal surfaces with bounded Morse index.
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@inproceedings{haozhao2016existence,
  title={Existence of minimal surfaces of arbitrary large Morse index},
  author={Haozhao L, and Xin Zhou},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161010110120661725109},
  booktitle={Calculus of Variations and Partial Differential Equations},
  volume={55},
  number={64},
  year={2016},
}
Haozhao L, and Xin Zhou. Existence of minimal surfaces of arbitrary large Morse index. 2016. Vol. 55. In Calculus of Variations and Partial Differential Equations. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161010110120661725109.
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