Existence of minimal surfaces of arbitrarily large Morse index
Author(s)Li, Haozhao; Zhou, Xin
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Calculus of Variations and Partial Differential Equations
Springer Berlin Heidelberg
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.
Author's final manuscript