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Total scalar curvature and rigidity of minimal hypersurfaces in Euclidean space
Published online by Cambridge University Press: 26 February 2010
Abstract
Let Mn, n ≥ 3, be a complete oriented minimal hypersurface in Euclidean space Rn+1. It is shown that, if the total scalar curvature on M is less than the n/2 power of 1/2Cs, where Cs is the Sobolev constant for M, and the square norm of the second fundamental form is a L2 function, then M is a hyperplane.
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- Research Article
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- Copyright © University College London 2001