On rigidity of the ideal boundary of an infinite riemann surface
On rigidity of the ideal boundary of an infinite riemann surface
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DOI：
10.1080/17476939008814414
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发表时间：
1990-04
期刊：
影响因子：
--
通讯作者：
M. Taniguchi
中科院分区：
文献类型：
--
作者：
M. Taniguchi
称无限黎曼曲面R的端点D是刚性的，如果R的每个拟共形自映射，与R上的恒等式同伦，在D上共形，实际上等于D上的恒等式。如果存在R的刚性端点的决定序列，我们说R有一个刚性理想边界点。具有刚性理想边界点的黎曼曲面的Teichmuller空间与有限黎曼曲面的Teichmuller空间形成对比。R是Fuchsian模型为第一类的Riemann曲面。然后证明了R有刚性理想边界点，或者当R包含一个无限平面端点，或者当R是一个平面区域的无限分支两层覆盖，或者当R允许一个绿色函数。
An end D of an infinite Riemann surface R is called to be rigid if every quasiconformal self-mapping of R, homotopic to the identity on R and conformal on D, is actually equal to the identity on D. If there is a determining sequence of rigid ends of R, we say that R has a rigid ideal boundary point. The Teichmuller space of a Riemann surface having a rigid ideal boundary point contrasts with that of a finite Riemann surface. Lei R be a Riemann surface whose Fuchsian model is of the first kind. Then we show that R has a rigid ideal boundary point, either if R contains an infinite planar end, or if R is an infinitely branched two-sheeted covering of a planar region, or if R admits a Green's function.