Existence of minimal surfaces of arbitrarily large Morse index
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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.
Date issued
2016-05Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Calculus of Variations and Partial Differential Equations
Publisher
Springer Berlin Heidelberg
Citation
Li, Haozhao, and Xin Zhou. “Existence of Minimal Surfaces of Arbitrarily Large Morse Index.” Calculus of Variations and Partial Differential Equations 55.3 (2016): n. pag.
Version: Author's final manuscript
ISSN
0944-2669
1432-0835