Abstract: The following question is answered negatively: Let φ be holomorphic in the unit disk Δ. If an extremal Teichmüller mapping f on Δ has complex dilatation μ_f=kφ/|φ|, can one say that μ_f has a Hamilton sequence such as {φ(t_nz)/‖φ(t_nz)‖:lim_n→∞t_n=1, t_n∈(0,1)}?

Key words: Hamilton sequence, Teichmüller mapping, extremality

摘要： 通过构造一定的反例，给出下面问题一个否定的回答：假设 φ 在单位圆盘 Δ 上全纯，并且极值的 Teichmüller 映射 f 具有复扩张 μ_f=kφ/|φ| ，那么 μ_f 是否有一个 Hamilton 序列形如 {φ(t_nz)/‖φ(t_nz)‖:lim_n→∞t_n=1, t_n∈(0,1)}?

关键词: Hamilton序列, Teichmüller映射, 极值性