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Total scalar curvature and rigidity of minimal hypersurfaces in Euclidean space
Author(s) -
Yun Gabjin
Publication year - 2001
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014479
Subject(s) - mathematics , hypersurface , hyperplane , scalar curvature , second fundamental form , mean curvature , mathematical analysis , euclidean space , curvature , prescribed scalar curvature problem , rigidity (electromagnetism) , euclidean geometry , pure mathematics , combinatorics , geometry , sectional curvature , physics , quantum mechanics
Let M n , n ≥ 3, be a complete oriented minimal hypersurface in Euclidean space R n +1 . It is shown that, if the total scalar curvature on M is less than the n /2 power of 1/2 C s , where C s is the Sobolev constant for M , and the square norm of the second fundamental form| A | 2is a L 2 function, then M is a hyperplane.
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