Existence of minimal surfaces of arbitrary large Morse index

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.

One figure, final version

References in corpus (3)

• New applications of Min-max Theory
• Compactness of minimal hypersurfaces with bounded index
• Minimal surfaces - variational theory and applications

Cited by in corpus (1)

• Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature