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渐近Teichmüller空间的不唯一性
Nonuniqueness Properties on Asymptotic Teichmuller Space
设AT（Δ）是单位圆盘Δ上所有渐近Teichmüller等价类[[μ]]或[[fμ]]构成的渐近Teichmüller空间.本文证明了对AT（Δ）内的任意渐近极值的fμ，总存在一个[[fμ]]内的渐近极值映射gν，使边界伸缩商h*（μf?g-1（g（z））}）≠0.同时也获得了AT（Δ）在基点处的切空间上的类似结果.
Let AT (Δ) be the asymptotic Teichmüller space on the unit disk Δ, viewed as the space of all asymptotic Teichmüller equivalence classes[[μ]] or[[f μ]]. It is shown that, for each asymptotically extremal[[f μ]] in AT (Δ), there exists an asymptotically extremal gν in[[f μ]] such that the boundary dilatation h*(μf?g-1(g(z))) =0. A parallel result in the tangent space to AT (Δ) at the basepoint is also obtained.
Teichmü / ller空间 / 拟共形映射 / 极值映射 / 渐近Teichmü / ller空间 {{custom_keyword}} /
Teichmüller space / quasiconformal mappings / extremal quasiconformal mappings / asymptotic Teichmüller space {{custom_keyword}} /
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