Symmetry of hypersurfaces of constant mean curvature with symmetric boundary (Q1057505)

Let S be a compact \(C^ 2\)-hypersurface in \(R^{n+1}\) with the (n-1)- dimensional sphere \(\Gamma_ 0\) as its boundary and of constant mean curvature. This paper proves that if S does not intersect with the outside of \(\Gamma_ 0\) in the hyperplane including \(\Gamma_ 0\), then S must be a spherical cap or the n-dimensional ball bounded by \(\Gamma_ 0\). Moreover, it gives a result on symmetry of constant mean curvature hypersurfaces bounded by more general symmetric boundaries.