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arXiv · 2010.02581

On holomorphic matrices on bordered Riemann surfaces

Jürgen Leiterer
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Abstract

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.

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Jürgen Leiterer. 2020-10-06. On holomorphic matrices on bordered Riemann surfaces. https://doi.org/10.1112/blms.12470

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