Index and topology of minimal hypersurfaces in \(\mathbb {R}^n\)

DOI10.1007/s00526-017-1272-zzbMath1380.53066arXiv1605.09693OpenAlexW2767601555MaRDI QIDQ1688788

Chao Li

Publication date: 11 January 2018

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1605.09693

zbMATH Keywords

finite total curvatureMorse indexBetti numberfinite index

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (6)

Quantitative index bounds for translators via topology ⋮ Lower bounds for the index of compact constant mean curvature surfaces in \(\mathbb{R}^3\) and \(\mathbb S^3\) ⋮ A note on the index of closed minimal hypersurfaces of flat tori ⋮ Index estimate of self-shrinkers in $\mathbb {R}^3$ with asymptotically conical ends ⋮ Index one minimal surfaces in spherical space forms ⋮ Index and first Betti number of \(f\)-minimal hypersurfaces and self-shrinkers

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the topology and index of minimal surfaces
• Index, vision number and stability of complete minimal surfaces
• The topology of complete minimal surfaces of finite total Gaussian curvature
• On complete minimal surfaces with finite Morse index in three manifolds
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• A complete embedded minimal surface in \({\mathbb{R}}^ 3\) with genus one and three ends
• Harmonic maps and the topology of stable hypersurfaces and manifolds with non-negative Ricci curvature
• On the existence of higher dimensional Enneper's surface
• \(L^ 2\) harmonic forms and stability of minimal hypersurfaces
• The structure of stable minimal hypersurfaces in \(\mathbb{R}^{n+1}\)
• Minimal hypersurfaces with finite index
• Higher dimensional Schwarz's surfaces and Scherk's surfaces
• Compactness of minimal hypersurfaces with bounded index
• Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals
• Complete minimal surfaces with index one and stable constant mean curvature surfaces
• On minimal hypersurfaces with finite harmonic indices
• Minimal hypersurfaces foliated by spheres
• Minimal hypersurfaces with bounded index
• One-sided complete stable minimal surfaces
• Index bounds for minimal hypersurfaces of the sphere
• Stability properties for the higher dimensional catenoid in $\mathbb R^{n+1}$
• Index and nullity of the Gauss map of the Costa-Hoffman-Meeks surfaces
• Rotation Hypersurfaces in Spaces of Constant Curvature
• Finiteness of Index and Total Scalar Curvature for Minimal Hypersurfaces
• On stable complete minimal hypersurfaces in R n +1
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
• Stable complete minimal surfaces in 𝑅³ are planes
• Example of a complete minimal immersion in IR3 of genus one and three-embedded ends
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ
• Embedded minimal surfaces of finite topology

This page was built for publication: Index and topology of minimal hypersurfaces in \(\mathbb {R}^n\)