no. 2
Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 2, pp. 461-469.

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

Classification : 53C24, 53C27, 53C55, 58J60 
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Boualem, Hassan; Herzlich, Marc. Rigidity at infinity for even-dimensional asymptotically complex hyperbolic spaces. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 2, pp. 461-469. http://www.numdam.org/item/ASNSP_2002_5_1_2_461_0/

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