ScholarLens Back to search
2021•Bulletin of the London Mathematical SocietyOpen access

On holomorphic matrices on bordered Riemann surfaces

Jürgen Leiterer

Open full text 4 citations

Abstract

Let D be the unit disk. Kutzschebauch and Studer (Bull. Lond. Math. Soc. 51 (2019) 995–1004) recently proved that, for each continuous map A : D ¯ → SL ( 2 , C ) , which is holomorphic in D, there exist continuous maps E , F : D ¯ → sl ( 2 , C ) , which are holomorphic in D, such that A = e E e F . Also they asked if this extends to arbitrary compact bordered Riemann surfaces. We prove that this is possible.

Open-access reader

About this research paper

What this paper is about

Let D be the unit disk. Kutzschebauch and Studer (Bull. Lond. Math. Soc. 51 (2019) 995–1004) recently proved that, for each continuous map A : D ¯ → SL ( 2 , C ) , which is holomorphic in D, there exist continuous maps E , F : D ¯ → sl ( 2 , C ) , which are holomorphic in D, such that A = e E e F . Also they asked if this extends to arbitrary compact bordered Riemann surfaces. We prove that this is possible.

Why it matters

OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Let D be the unit disk. Kutzschebauch and Studer (Bull. Lond. Math. Soc. 51 (2019) 995–1004) recently proved that, for each continuous map A : D ¯ → SL ( 2 , C ) , which is holomorphic in D, there exist continuous maps E , F : D ¯ → sl ( 2 , C ) , which are holomorphic in D, such that A = e E e F . Also they asked if this extends to arbitrary compact bordered Riemann surfaces. We prove that this is possible.

Key concepts: Holomorphic function, Mathematics, Riemann surface, Unit disk, Pure mathematics, Riemann hypothesis, Mathematical analysis

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On holomorphic matrices on bordered Riemann surfaces — Research Paper | ScholarLens