A classical theorem of A. D. Alexandrov characterized round spheres is extended to the complex hyperbolic space CH2 of constant holomorphic sectional curvature. A detailed description of the horospheres and equidistant hypersurfaces in CH2 determining in particular their stability, is also given.
Transactions of the American Mathematical Society. Providence. Vol. 339, no. 2 (oct. 1993), p. 685-702.