This paper presents some rigidity results about compact hypersurfaces with free
boundary in a wedge in a space form. First, we prove that every compact immersed
stable constant mean curvature hypersurface with free boundary in a wedge is part of
an intrinsic sphere centered at a point of the edge of the wedge. Second, we show that
the same rigidity result holds for a compact embedded constant higher-order mean
curvature hypersurface with free boundary in a wedge. Finally, we extend this result
to a compact immersed hypersurface with free boundary in a wedge that has the
additional property that the ratio of two higher-order mean curvatures is
constant.
The same conclusions hold for a compact hypersurface with free boundary that
lies in a half-space in a space form.
Dedicated to Professor Jaigyoung Choe
in honor of his 65th birthday.
Keywords
intrinsic spheres, surfaces with free boundary,
higher-order mean curvature
