L 2 harmonic forms and finiteness of ends

DOI10.1590/S0001-37652013000200003zbMath1307.53032MaRDI QIDQ2865807

Peng Zhu

Publication date: 3 December 2013

Published in: Anais da Academia Brasileira de Ciências (Search for Journal in Brave)

Full work available at URL: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0001-37652013000200457&lng=en&nrm=iso&tlng=en

zbMATH Keywords

\(L^2\)-harmonic formsweighted Poincaré inequality

Mathematics Subject Classification ID

Differential geometric aspects of harmonic maps (53C43) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (2)

Finiteness of non-parabolic ends on submanifolds in spheres ⋮ \(L^{2}\) harmonic 1-forms on minimal submanifolds in spheres

Cites Work

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• The structure of weakly stable constant mean curvature hypersurfaces
• One end theorem and application to stable minimal hypersurfaces
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• Minimal hypersurfaces with finite index
• Complete manifolds with positive spectrum
• The heat equation and harmonic maps of complete manifolds
• Spectrum of the Laplacian on quaternionic Kähler manifolds
• Results on a weighted Poincaré inequality of complete manifolds
• Weighted Poincaré inequality and rigidity of complete manifolds
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• Differential equations on riemannian manifolds and their geometric applications
• L 2 harmonic forms and stability of hypersurfaces with constant mean curvature

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