Almost spherical convex hypersurfaces

John Douglas Moore
1973 Transactions of the American Mathematical Society  
Let M be a smooth compact hypersurface with positive sectional curvatures in zz-dimensional euclidean space. This paper gives a sufficient condition for M to lie in the spherical shell bounded by concentric spheres of radius 1 -í and 1 + e. This condition is satisfied, in the case where z¡ = 3, if the Gaussian curvature or the mean curvature of M is sufficiently pointwise close to one.
doi:10.1090/s0002-9947-1973-0320964-2 fatcat:a6ieut7wy5atvd6zwicfxtb3xq