• Journal of the Korean Mathematical Society
• /
• v.44 no.6
• /
• pp.1291-1312
• /
• 2007

We study some extremal problems on the Cartan-Hartogs domains. Through computing the minimal circumscribed Hermitian ellipsoid of the Cartan-Hartogs domains, we get the $Carath\acute{e}odory$ extremal mappings between the Cartan-Hartogs domains and the unit hyperball, and the explicit formulas for computing the $Carath\acute{e}odory$ extremal value.

• Journal of the Korean Mathematical Society
• /
• v.54 no.6
• /
• pp.1683-1698
• /
• 2017

In this paper, we study the $Carath{\acute{e}}odory$ extremal problems on the Hua domain of the first three types. We give the explicit formula for the $Carath{\acute{e}}odory$ extremal problems between the first three types of Hua domain and the unit ball, which improves the works done on Hua domain and Cartan-egg domain and super-Cartan domain.