The mean curvature and volume growth of complete noncompact submanifolds

DOI10.1016/S0926-2245(98)00010-2zbMath0942.53037WikidataQ115337503 ScholiaQ115337503MaRDI QIDQ1295454

Pui-Fai Leung, Leung-Fu Cheung

Publication date: 24 June 1999

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

zbMATH Keywords

volume growthbounded mean curvatureparallel mean curvature

Mathematics Subject Classification ID

Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20)

Related Items (10)

Weighted volume growth and vanishing properties of \(f\)-minimal hypersurfaces in a weighted manifold ⋮ Sobolev and isoperimetric inequalities for submanifolds in weighted ambient spaces ⋮ Weighted \(L^2\) harmonic 1-forms and the topology at infinity of complete noncompact weighted manifolds ⋮ Isoperimetric inequalities for submanifolds with bounded mean curvature ⋮ Mean curvature, volume and properness of isometric immersions ⋮ Minimal submanifolds in a metric measure space ⋮ Skew mean curvature flow ⋮ The non-parabolicity of infinite volume ends ⋮ Isoperimetric inequalities for submanifolds. Jellett-Minkowski's formula revisited ⋮ On the structure and volume growth of submanifolds in Riemannian manifolds

Cites Work

• On square integrability of mean curvature for surfaces with positive Gaussian curvature
• Complete surfaces of constant mean curvature-1 in the hyperbolic 3-space
• Sobolev and isoperimetric inequalities for riemannian submanifolds
• Sobolev and mean‐value inequalities on generalized submanifolds of Rⁿ
• Unnamed Item

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