Morse index bounds for minimal submanifolds

DOI10.1007/s13348-022-00380-7MaRDI QIDQ6141127

Diego Adauto, Márcio Batista

Publication date: 22 January 2024

Published in: Collectanea Mathematica (Search for Journal in Brave)

zbMATH Keywords

submanifoldsMorse indexBetti numberhigh codimension

Mathematics Subject Classification ID

Eigenvalue problems for linear operators (47A75) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Variational methods for eigenvalues of operators (49R05)

Cites Work

• Index and first Betti number of \(f\)-minimal hypersurfaces and self-shrinkers
• Stable minimal submanifolds in compact rank one symmetric spaces
• Second variation of compact minimal Legendrian submanifolds of the sphere
• Compact minimal hypersurfaces with index one in the real projective space
• Comparing the Morse index and the first Betti number of minimal hypersurfaces
• On stable currents and their application to global problems in real and complex geometry
• Minimal hypersurfaces with low index in the real projective space
• Lower bounds for the index of compact constant mean curvature surfaces in \(\mathbb{R}^3\) and \(\mathbb S^3\)
• Index estimates for surfaces with constant mean curvature in 3-dimensional manifolds
• Robust index bounds for minimal hypersurfaces of isoparametric submanifolds and symmetric spaces
• Minimal varieties in Riemannian manifolds
• Quantitative index bounds for translators via topology
• Minimal Surfaces with Low Index in the Three-Dimensional Sphere
• Index bounds for minimal hypersurfaces of the sphere
• Index estimates for closed minimal submanifolds of the sphere
• New applications of Min-max Theory
• On stable compact minimal submanifolds
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