The circle pattern uniformization problem

Abstract The existence of an explicit and canonical cell decomposition of the moduli space of closed Riemann surfaces of genus two shows that each Riemann surface of genus two can be parametrised by a 12-tuple of real numbers which corresponds to the angle coordinates of a graph associated to the su...

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Autores principales:	Amaris,Armando Rodado, Lusares,Gina
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2017
Materias:	Uniformization Problem Riemann Surfaces of Genus Two Circle pattern Uniformization Problem
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300397
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spelling	oai:scielo:S0716-091720170003003972017-10-31The circle pattern uniformization problemAmaris,Armando RodadoLusares,Gina Uniformization Problem Riemann Surfaces of Genus Two Circle pattern Uniformization Problem Abstract The existence of an explicit and canonical cell decomposition of the moduli space of closed Riemann surfaces of genus two shows that each Riemann surface of genus two can be parametrised by a 12-tuple of real numbers which corresponds to the angle coordinates of a graph associated to the surface. This suggests a Circle Pattern Uniformization Problem that we have defined and solved for three classical Riemann surfaces of genus two. Although in general, finding the exact algebraic equations corresponding to a hyperbolic surface from angle coordinates is a hard problem, we prove that known numerical methods can be applied to find approximated equations of Riemann surfaces of genus two from their angle coordinates and graph data for a large family of Riemann surfaces of genus two.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.36 n.3 20172017-09-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300397en10.4067/S0716-09172017000300397
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Uniformization Problem Riemann Surfaces of Genus Two Circle pattern Uniformization Problem
spellingShingle	Uniformization Problem Riemann Surfaces of Genus Two Circle pattern Uniformization Problem Amaris,Armando Rodado Lusares,Gina The circle pattern uniformization problem
description	Abstract The existence of an explicit and canonical cell decomposition of the moduli space of closed Riemann surfaces of genus two shows that each Riemann surface of genus two can be parametrised by a 12-tuple of real numbers which corresponds to the angle coordinates of a graph associated to the surface. This suggests a Circle Pattern Uniformization Problem that we have defined and solved for three classical Riemann surfaces of genus two. Although in general, finding the exact algebraic equations corresponding to a hyperbolic surface from angle coordinates is a hard problem, we prove that known numerical methods can be applied to find approximated equations of Riemann surfaces of genus two from their angle coordinates and graph data for a large family of Riemann surfaces of genus two.
author	Amaris,Armando Rodado Lusares,Gina
author_facet	Amaris,Armando Rodado Lusares,Gina
author_sort	Amaris,Armando Rodado
title	The circle pattern uniformization problem
title_short	The circle pattern uniformization problem
title_full	The circle pattern uniformization problem
title_fullStr	The circle pattern uniformization problem
title_full_unstemmed	The circle pattern uniformization problem
title_sort	circle pattern uniformization problem
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2017
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172017000300397
work_keys_str_mv	AT amarisarmandorodado thecirclepatternuniformizationproblem AT lusaresgina thecirclepatternuniformizationproblem AT amarisarmandorodado circlepatternuniformizationproblem AT lusaresgina circlepatternuniformizationproblem
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The circle pattern uniformization problem

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