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

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