Vanishing theorems for $L^2$ harmonic 1-forms on complete submanifolds in a Riemannian manifold (Q472366)

scientific article; zbMATH DE number 6370956

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English	Vanishing theorems for $L^2$ harmonic 1-forms on complete submanifolds in a Riemannian manifold	scientific article; zbMATH DE number 6370956

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instance of

scholarly article

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title

Vanishing theorems for $L^2$ harmonic 1-forms on complete submanifolds in a Riemannian manifold (English)

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Journal of Mathematical Analysis and Applications

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publication date

19 November 2014

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zbMATH Keywords

$\delta$-stability inequality

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$L^2$ harmonic 1-form

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traceless second fundamental form

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first eigenvalue

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MaRDI profile type

Publication

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full work available at URL

https://doi.org/10.1016/j.jmaa.2014.10.076

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cites work

$L^2$-cohomology and Sobolev inequalities

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$L^2$-harmonic 1-forms on submanifolds with finite total curvature

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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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Stable complete minimal surfaces in 𝑅³ are planes

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Q3041926

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Stable minimal hypersurfaces in a Riemannian manifold with pinched negative sectional curvature

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The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature

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The structure of $\delta $-stable minimal hypersurfaces in $\mathbb{R}^{n+1}$

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$L^2$ harmonic 1-forms on complete submanifolds in Euclidean space

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Vanishing theorems on complete manifolds with weighted Poincaré inequality and applications

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On the existence of a Green's function on a manifold

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ON THE EXISTENCE OF POSITIVE FUNDAMENTAL SOLUTIONS OF THE LAPLACE EQUATION ON RIEMANNIAN MANIFOLDS

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Sobolev and isoperimetric inequalities for riemannian submanifolds

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Q3948276

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Operator $\Delta$-aK on surfaces

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On the structure of complete hypersurfaces in a Riemannian manifold of nonnegative curvature and $L^2$ harmonic forms

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An Estimate on the Ricci Curvature of a Submanifold and Some Applications

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The complete hyper-surfaces with zero scalar curvature in $\mathbb{R}^{n+1}$

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Liouville-type properties for embedded minimal surfaces

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Q4218995

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Gap theorems for minimal submanifolds in $\mathbb{R}^{n+1}$

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Stability of minimal hypersurfaces

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Minimal submanifolds with small total scalar curvature in Euclidean space

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Rigidity of minimal submanifolds in hyperbolic space

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$L^{2}$ harmonic 1-forms on minimal submanifolds in hyperbolic space

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On stable complete minimal hypersurfaces in R n +1

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Stability properties for the higher dimensional catenoid in $\mathbb R^{n+1}$

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Q3223122

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On conformally compact Einstein manifolds.

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On minimal submanifolds in an Euclidean space

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Q4102442

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Total scalar curvature and $L^2$ harmonic 1-forms on a minimal hypersurface in Euclidean space

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Identifiers

zbMATH Open document ID

1303.53067

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Mathematics Subject Classification ID

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10.1016/J.JMAA.2014.10.076

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Sitelinks

Mathematics(1 entry)

mardi Publication:472366

Vanishing theorems for \(L^2\) harmonic 1-forms on complete submanifolds in a Riemannian manifold (Q472366)

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Identifiers

Sitelinks

Mathematics(1 entry)