On stable minimal surfaces in manifolds of positive bi-Ricci curvatures

DOI10.1215/S0012-7094-96-08505-1zbMath0874.53049OpenAlexW1495083299MaRDI QIDQ1816471

Rugang Ye, Ying Shen

Publication date: 11 November 1997

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-96-08505-1

zbMATH Keywords

bi-Ricci curvatureclosed stable minimal hypersurface

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items

\(L_{f}\)-index bounds for closed \(f\)-minimal hypersurfaces, L 2 harmonic forms and stability of hypersurfaces with constant mean curvature, Vanishing theorems for \(L^{2}\) harmonic forms on complete Riemannian manifolds, Stably embedded minimal hypersurfaces, A generalization of Geroch's conjecture, Two rigidity results for stable minimal hypersurfaces, Unnamed Item, The structure of weakly stable constant mean curvature hypersurfaces, Harmonic 1-forms on immersed hypersurfaces in a Riemannian manifold with weighted bi-Ricci curvature bounded from below, \(L^2\) harmonic forms on a complete stable hypersurfaces with constant mean curvature, Graphical mean curvature flow with bounded bi-Ricci curvature

Cites Work

• The existence of a black hole due to condensation of matter
• On the structure of manifolds with positive scalar curvature
• The classification of simply connected manifolds of positive scalar curvature
• The Jacobi equation on naturally reductive compact Riemannian homogeneous spaces
• The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
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