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We study the boundary behavior of the Kobayashi--Fuks metric on the class ofh-extendible domains. Here, we derive the non-tangential boundary asymptoticsof the Kobayashi--Fuks metric and its Riemannian volume element by the help ofsome maximal domain functions and then using their stability results onh-extendible local models.

Weighted boundary limits of the Kobayashi--Fuks metric on h-extendible domains