Qualitative and quantitative estimates for minimal hypersurfaces with bounded index and area

DOI10.1090/tran/7168zbMath1390.53008arXiv1512.01047OpenAlexW2963713408WikidataQ59883693 ScholiaQ59883693MaRDI QIDQ4608782

Ben Sharp, Reto Buzano

Publication date: 28 March 2018

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1512.01047

zbMATH Keywords

Ricci curvatureMorse indexminimal hypersurfacestotal curvatureclosed Riemannian manifoldJacobi (second variation) operator

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (9)

Minimal hypersurfaces with bounded index ⋮ CMC hypersurfaces with bounded Morse index ⋮ On the topology and index of minimal surfaces. II ⋮ Geometry of CMC surfaces of finite index ⋮ Morse index, Betti numbers, and singular set of bounded area minimal hypersurfaces ⋮ Bubble-tree convergence and local diffeomorphism finiteness for gradient Ricci shrinkers ⋮ Geometric convergence results for closed minimal surfaces via bubbling analysis ⋮ Curvature estimates and sheeting theorems for weakly stable CMC hypersurfaces ⋮ Bubbling analysis and geometric convergence results for free boundary minimal surfaces

Cites Work

• Unnamed Item
• A lower bound for the number of negative eigenvalues of Schrödinger operators
• Compactness of the space of minimal hypersurfaces with bounded volume and \(p\)-th Jacobi eigenvalue
• On the topology and index of minimal surfaces
• The strong halfspace theorem for minimal surfaces
• On the Schrödinger equation and the eigenvalue problem
• On complete minimal surfaces with finite Morse index in three manifolds
• Uniqueness, symmetry, and embeddedness of minimal surfaces
• The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature
• Schrödinger operators and index bounds for minimal submanifolds
• Elliptic partial differential equations of second order
• Minimal hypersurfaces with finite index
• Compactness of minimal hypersurfaces with bounded index
• Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals
• The Bochner formula for isometric immersions
• Existence of infinitely many minimal hypersurfaces in positive Ricci curvature
• Minimal hypersurfaces with bounded index
• Min-max theory and the Willmore conjecture
• Existence and regularity almost everywhere of solutions to elliptic variational problems among surfaces of varying topological type and singularity structure
• Minimal varieties in Riemannian manifolds
• Minimal Surfaces with Low Index in the Three-Dimensional Sphere
• Comparison between second variation of area and second variation of energy of a minimal surface
• Finiteness of Index and Total Scalar Curvature for Minimal Hypersurfaces
• Regularity of stable minimal hypersurfaces
• Compactness of spaces of propely embedded minimal surfaces with finite total curvature

This page was built for publication: Qualitative and quantitative estimates for minimal hypersurfaces with bounded index and area