Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces

摘要

Any Kaehler metric on the ball which is strongly asymptotic to complexhyperbolic space and whose scalar curvature is no less than the one of thecomplex hyperbolic space must be isometrically biholomorphic to it. This resulthas been known for some time in odd complex dimension and we provide here aproof in even dimension.