Non-existence of stable currents in submanifolds of the Euclidean spaces

DOI10.1007/s00022-010-0024-4zbMath1208.53062OpenAlexW1999589829MaRDI QIDQ5962042

Qiuyan Zhang, Jiancheng Liu

Publication date: 16 September 2010

Published in: Journal of Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00022-010-0024-4

zbMATH Keywords

second fundamental formmean curvatureprincipal curvaturemean curvature stable currentstable current

Mathematics Subject Classification ID

Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global submanifolds (53C40)

Related Items (4)

The Lawson-Simons' theorem on warped product submanifolds with geometric information ⋮ On the topology of CR-warped product submanifolds ⋮ Stable currents and homology groups in a compact CR-warped product submanifold with negative constant sectional curvature ⋮ Homology of submanifolds of six dimensional sphere

Cites Work

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• Stable minimal submanifolds in compact rank one symmetric spaces
• Non-existence of stable currents in hypersurfaces
• On stable currents and their application to global problems in real and complex geometry
• Nonexistence of stable currents
• Normal and integral currents
• On a relation between the topology and the intrinsic and extrinsic geometries of a compact submanifold
• An Estimate on the Ricci Curvature of a Submanifold and Some Applications
• The RICCI curvature of submanifolds and its applications
• Homology Spheres Which are Covered by Spheres
• Scalar Curvature, Inequality and Submanifold

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