Min-max theory for free boundary minimal hypersurfaces. II: General Morse index bounds and applications

DOI10.1007/s00208-020-02096-0zbMath1466.53074arXiv1907.12064OpenAlexW3093936664MaRDI QIDQ2664157

Xin Zhou, Qiang Guang, Zhichao Wang, Martin Man-Chun Li

Publication date: 20 April 2021

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1907.12064

zbMATH Keywords

minimal hypersurfaceMorse indexfree boundarymin-max theory

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (15)

The viscosity method for min-max free boundary minimal surfaces ⋮ Existence of minimal hypersurfaces with non-empty free Boundary for generic metrics ⋮ Compactness and generic finiteness for free boundary minimal hypersurfaces. I ⋮ Min-max theory for free boundary G-invariant minimal hypersurfaces ⋮ Mean curvature and variational theory ⋮ Equivariant index bound for min-max free boundary minimal surfaces ⋮ Inequivalent complexity criteria for free boundary minimal surfaces ⋮ A free boundary minimal surface via a 6-sweepout ⋮ Estimating the Morse index of free boundary minimal hypersurfaces through covering arguments ⋮ Multiplicity one for min-max theory in compact manifolds with boundary and its applications ⋮ Existence of infinitely many free boundary minimal hypersurfaces ⋮ Existence of infinitely many minimal hypersurfaces in closed manifolds ⋮ The relative isoperimetric inequality for minimal submanifolds with free boundary in the Euclidean space ⋮ Conformal upper bounds for the volume spectrum ⋮ A mountain-pass theorem for asymptotically conical self-expanders

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