Necessary conditions and nonexistence results for connected submanifolds in a Riemannian manifold

DOI10.1016/J.AIM.2017.09.038zbMath1377.49046OpenAlexW2760485996WikidataQ115362009 ScholiaQ115362009MaRDI QIDQ1673985

Keomkyo Seo

Publication date: 30 October 2017

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2017.09.038

zbMATH Keywords

nonexistencemean curvatureminimal submanifolddensity estimateBryant surface

Mathematics Subject Classification ID

Minimal surfaces and optimization (49Q05) Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

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• Doubly-connected minimal surfaces
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• Mean curvature one surfaces in hyperbolic space, and their relationship to minimal surfaces in Euclidean space
• Embeddedness of minimal surfaces with total boundary curvature at most \(4\pi\)
• Maximum principles for submanifolds of arbitrary codimension and bounded mean curvature
• A supplement to the condition of J. Douglas
• Complete minimal surfaces in \(S^ 3\)
• Maximum principles for minimal surfaces and for surfaces of continuous mean curvature
• The isoperimetric inequality for minimal surfaces in a Riemannian manifold
• Three theorems on manifolds with bounded mean curvature
• On new results in the theory of minimal surfaces
• Note on the Nonexistence of Minimal Surfaces

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