The extremal problem can be considered to be a similar to the classical Schwarz lemma [Tr] and also considered as an extension of the classical Schwarz lemma in high dimensions [Mal]. The extremal problem means the following problem: Let M be a domain in C~n and p ∈ M . Let M_p denote the couple (M, p), a pointed domain. For two pointed domains M_p and N_q, let Hol(M_p,N_q) denote the set of holomorphic mappings from M to N that send p to q. A mapping f ∈ Hol(M_p, N_q) is said to be Caratheodory extremal mapping, if |det df(p)| = sup{|det dg(p)| : g ∈ Hol(M_p,N_q)}, and now |det df(p)| is called to be Caratheodory extremal value. Simply, we call them c-extremal marting and c-extremal value respectively.
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机译：极端问题可以被认为是类似于古典施瓦茨的引理[Tr]，也被认为是高尺寸的古典施瓦茨引理的延伸[MAL]。 极值问题意味着以下问题：让M是C〜n和p∈m中的域。 让M_P表示耦合（m，p），尖域。 对于两个尖端的域M_P和N_Q，让HOL（M_P，N_Q）表示从M到N向Q发送P到Q的全象映射集。 据说映射F∈HOL（M_P，N_Q）是加工漫步的极值映射，IF | DET DF（P）| = sup {| det dg（p）| ：g∈hol（m_p，n_q）}，现在| det df（p）| 被称为加工漫步的极值价值。 简单地，我们分别称为C-Extremal Marting和C-极值。
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