CHEN'S CONJECTURE AND ε-SUPERBIHARMONIC SUBMANIFOLDS OF RIEMANNIAN MANIFOLDS

DOI10.1142/S0129167X13500286zbMath1277.53059arXiv1305.5294OpenAlexW3098410208WikidataQ115246525 ScholiaQ115246525MaRDI QIDQ5300017

Glen Wheeler

Publication date: 24 June 2013

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1305.5294

zbMATH Keywords

harmonic mean curvatureminimal immersionbiharmonic submanifold

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Global Riemannian geometry, including pinching (53C20) Differential geometric aspects of harmonic maps (53C43) Surfaces in Euclidean and related spaces (53A05)

Related Items (10)

Biharmonic maps from tori into a 2-sphere ⋮ Some recent progress of biharmonic submanifolds ⋮ Theory and numerics for Chen's flow of curves ⋮ Analysis of the inhomogeneous Willmore equation ⋮ Biharmonic hypersurfaces in a sphere ⋮ Topics in differential geometry associated with position vector fields on Euclidean submanifolds ⋮ Biharmonic maps from a complete Riemannian manifold into a non-positively curved manifold ⋮ On biharmonic submanifolds in non-positively curved manifolds ⋮ A rigidity theorem for ideal surfaces with flat boundary ⋮ Biharmonic submanifolds in manifolds with bounded curvature

Cites Work

• Biharmonic lifts by means of pseudo-Riemannian submersions in dimension three
• BIHARMONIC PSEUDO-RIEMANNIAN SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACES
• BIHARMONIC SUBMANIFOLDS OF ${\mathbb S}^3$
• Hypersurfaces in E⁴ with Harmonic Mean Curvature Vector Field
• On a Question of Hadamard Concerning Super‐Biharmonic Functions

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