渐近Teichmüller空间的不唯一性

Nonuniqueness Properties on Asymptotic Teichmuller Space

设AT(△)是单位圆盘△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(△)内的任意渐近极值的fμ,总存在一个[[fμ]]内的渐近极值映射gv,使边界伸缩商h*(μfog-1(g(z)))≠0.同时也获得了AT(△)在基点处的切空间上的类似结果.

Let AT(△)be the asymptotic Teichmuller space on the unit disk△,viewed as the space of all asymptotic Teichmuller equivalence classes[[μ]]or[[fμ]].It is shown that,for each asymptotically extremal[[fμ]]in AT(△),there exists an asymptotically extremal gv in[[fμ]]such that the boundary dilatation h*(μfog-1(g(z)))≠0.A parallel result in the tangent space to AT(△)at the basepoint is also obtained.