Morse index, Betti numbers, and singular set of bounded area minimal hypersurfaces (Q6177380)

scientific article; zbMATH DE number 7732803

Language	Label	Description	Also known as
English	Morse index, Betti numbers, and singular set of bounded area minimal hypersurfaces	scientific article; zbMATH DE number 7732803

Statements

instance of

scholarly article

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title

Morse index, Betti numbers, and singular set of bounded area minimal hypersurfaces (English)

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author

Antoine Song

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published in

Duke Mathematical Journal

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publication date

31 August 2023

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full work available at URL

https://arxiv.org/abs/1911.09166

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https://projecteuclid.org/journals/duke-mathematical-journal/volume-172/issue-11/Morse-index-Betti-numbers-and-singular-set-of-bounded-area/10.1215/00127094-2023-0012.full

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zbMATH Keywords

Betti numbers

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minimal surfaces

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Morse index

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singular set

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MaRDI profile type

MaRDI publication profile

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cites work

Non-compactness of the space of minimal hypersurfaces

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Geometric convergence results for closed minimal surfaces via bubbling analysis

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Comparing the Morse index and the first Betti number of minimal hypersurfaces

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A note on the index of closed minimal hypersurfaces of flat tori

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Manifolds of nonpositive curvature

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

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Generic finiteness of minimal surfaces with bounded Morse index

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Minimal hyperspheres of arbitrarily large Morse index

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Regularity of Einstein manifolds and the codimension 4 conjecture

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Minimal hypersurfaces with bounded index

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Minimal surfaces and the Allen-Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates

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New minimal surfaces in \(\mathbb S^3\) desingularizing the Clifford tori

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The space of minimal embeddings of a surface into a three-dimensional manifold of positive Ricci curvature

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Singular limit laminations, Morse index, and positive scalar curvature

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The space of embedded minimal surfaces of fixed genus in a 3-manifold. I: Estimates off the axis for disks

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The space of embedded minimal surfaces of fixed genus in a 3-manifold. II: Multi-valued graphs in disks

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The space of embedded minimal surfaces of fixed genus in a 3-manifold. III: Planar domains

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The space of embedded minimal surfaces of fixed genus in a 3-manifold. IV: Locally simply connected

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The space of embedded minimal surfaces of fixed genus in a 3-manifold. V. Fixed genus

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Comparison between second variation of area and second variation of energy of a minimal surface

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The Allen-Cahn equation on closed manifolds

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Robust index bounds for minimal hypersurfaces of isoparametric submanifolds and symmetric spaces

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Curvature, diameter and Betti numbers

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Minimal cones and the spherical Bernstein problem. I

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Minimal cones and the spherical Bernstein problem. II

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Density of minimal hypersurfaces for generic metrics

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Q5486614

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Doubling and Desingularization Constructions for Minimal Surfaces

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Minimal surfaces in the round three-sphere by doubling the equatorial two-sphere. I

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Minimal Surfaces in the Round Three‐Sphere by Doubling the Equatorial Two‐Sphere, II

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The index and nullity of the Lawson surfaces \(\xi_{g,1}\)

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Minimal surfaces in the three-sphere by desingularizing intersecting Clifford tori

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Minimal surfaces in the three-sphere by doubling the Clifford torus

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The catenoid estimate and its geometric applications

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Complete minimal surfaces in \(S^ 3\)

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Existence of minimal surfaces of arbitrarily large Morse index

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Morse index and multiplicity of \(\min\text{-}\max\) minimal hypersurfaces

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Existence of infinitely many minimal hypersurfaces in positive Ricci curvature

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Morse index of multiplicity one min-max minimal hypersurfaces

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Equidistribution of minimal hypersurfaces for generic metrics

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Sharp asymptotics of the first eigenvalue on some degenerating surfaces

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Local removable singularity theorems for minimal laminations

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The singular structure and regularity of stationary varifolds

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Riemannian Geometry

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One-sided complete stable minimal surfaces

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Index bounds for minimal hypersurfaces of the sphere

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Q3314528

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Regularity of stable minimal hypersurfaces

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Curvature estimates for minimal hypersurfaces

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Compactness of minimal hypersurfaces with bounded index

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Stable minimal hypersurfaces in \(\mathbb{R}^{N+1+\ell}\) with singular set an arbitrary closed \(K\subset\{0\}\times\mathbb{R}^{\ell}\)

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Existence of infinitely many minimal hypersurfaces in closed manifolds

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Identifiers

arXiv ID

1911.09166

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DOI

10.1215/00127094-2023-0012

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6177380