Existence of minimal surfaces of arbitrarily large Morse index

  • Haozhao Li
  • Xin Zhou


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.

Mathematics Subject Classification

53A10 49Q05 58E12 53C42 



Part of this work was done while the first author was visiting MIT and he wishes to thank MIT for their generous hospitality. The second author wants to thank Toby Colding, Bill Minicozzi and Rick Schoen for helpful conversation on this work. Finally, we thank the referee for very useful comments.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Key Laboratory of Wu Wen-Tsun Mathematics, Chinese Academy of Sciences, School of Mathematical SciencesUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA

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