Existence of minimal surfaces of arbitrary large Morse index

Haozhao Li; Xin Zhou

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arXiv · 1504.00970

Existence of minimal surfaces of arbitrary large Morse index

Haozhao Li·Xin Zhou

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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 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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Haozhao Li, Xin Zhou. 2015-04-04. Existence of minimal surfaces of arbitrary large Morse index. https://arxiv.org/abs/1504.00970

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