论文标题
在边界的riemann表面上的全态矩阵上
On holomorphic matrices on bordered Riemann surfaces
论文作者
论文摘要
令$ \ d $为单位磁盘。 Kutzschebauch和Studer \ cite {ks}最近证明，对于每个连续地图$ a：\ overline d \ to \ mathrm {slrm {sl}（2，\ c）$，它在$ \ d $中是holomorphic in $ \ d $，存在连续的maps $ e，f：\ overline f：\ overline f：\ drline \ d \ d \ d \ d \ the \ the是2 \ the，\ d \ c c c c c c cank can $ \ d $中的holomorthic，因此$ a = e^ee^f $。他们还询问这是否扩展到任意紧凑的边界riemann表面。我们证明这是可能的。
Let $\D$ be the unit disk. Kutzschebauch and Studer \cite{KS} recently proved that, for each continuous map $A:\overline D\to \mathrm{SL}(2,\C)$, which is holomorphic in $\D$, there exist continuous maps $E,F:\overline \D\to \mathfrak{sl}(2,\C)$, which are holomorphic in $\D$, such that $A=e^Ee^F$. Also they asked if this extends to arbitrary compact bordered Riemann surfaces. We prove that this is possible.
