Total scalar curvature and rigidity of minimal hypersurfaces in Euclidean space

Abstract

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 1/2C s , where C s is the Sobolev constant for M, and the square norm of the second fundamental form |A| 2 is a L 2 function, then M is a hyperplane.