Existence of minimal surfaces of arbitrary large Morse index

2015/04/04 by Haozhao Li, Xin Zhou, Li, Haozhao +1
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1504.00970

One figure, final version

arxiv created 2016/05/24 · arxiv updated 2016/05/25

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 F. Marques and A. Neves. We prove this by analyzing the lamination structure of the limit of minimal surfaces with bounded Morse index.

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