Compactness of minimal hypersurfaces with bounded index

Abstract

We prove a compactness result for minimal hypersurfaces with bounded index and volume, which can be thought of as an extension of the compactness theorem of Choi-Schoen (Invent. Math. 1985) to higher dimensions.

arXiv comment17 pages

Cited by in corpus (6)

• Minimal hypersurfaces with bounded index
• Existence of minimal surfaces of arbitrary large Morse index
• Smooth compactness of $f$-minimal hypersurfaces with bounded $f$-index
• Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature
• Compactness of the space of minimal hypersurfaces with bounded volume and p-th Jacobi eigenvalue
• Bubbling analysis and geometric convergence results for free boundary minimal surfaces