  We establish an integral formula on a smooth, precompact domain in a Kahler
manifold. We apply this formula to study holomorphic extension of CR functions.
Using this formula we prove an isoperimetric inequality in terms of a positive
lower bound for the Hermitian curvature of the boundary. Combining with a
Minkowski type formula on the complex hyperbolic space we prove that any
closed, embedded hypersurface of constant mean curvature must be a geodesic
sphere, provided the hypersurface is Hopf. A similar result is established on
the complex projective space.
