The structure of complete stable minimal surfaces in 3-manifolds of non-negative scalar curvature
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Publication:3881522
DOI10.1002/cpa.3160330206zbMath0439.53060OpenAlexW1996561347WikidataQ29030439 ScholiaQ29030439MaRDI QIDQ3881522
D. Fischer-Colbrie, Richard M. Schoen
Publication date: 1980
Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1002/cpa.3160330206
Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)
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Cites Work