Existence of minimal surfaces of arbitrarily large Morse index

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Abstract

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 

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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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