Cartan-the Hartogs Domain Of The Extreme Value Problem

In this paper we study the extremal problem between the second type of Cartan-Hartogs domain and the unit hyperball. We get the Caratheodory extremal mappings from the second type of Cartan-Hartogs domain to the unit hyperball, and the explicit formulas for computing the Caratheodory extremal values and the extremal distances. Here is the form of the second type of Cartan-Hartogs domain:where R_II(p) denotes the second type of Cartan domain in the sense of L.K.Hua, Z is a symmetrical matrix of order p, Z^t denotes the transposed of Z, Z|- denotes the conjugate of Z, det denotes the determinant of a square matrix, N is a positive integer, and K is a positive real number.In order to find the Caratheodory extremal mappings from the second type of Cartan-Hartogs domain to the unit hyperball, we firstly get the general form of the minimal circumscribed Hermitian ellipsoid of Y_II(N;p;K):where M = Then according to the concrete form of the minimal circumscribed Hermitian ellipsoid of Y_II(N;p;K) in different situations, we get the following conclusions:When 0 < K ≤ p, the following mapping is the Caratheodory extremal mapping from Y_II(N,p,K) to the unit hyperball B^N+M:...