Diskretna interpretacija Riemannovega upodobitvenega izreka

delo diplomskega seminarja

Anja Kišek (Author), Uroš Kuzman (Mentor)

Abstract

V diplomskem delu bomo obravnavali diskretno interpretacijo Riemannovega upodobitvenega izreka oziroma alternativni postopek iskanja biholomorfizma med poljubno, pravo, enostavno povezano podmnožico kompleksne ravnine in enotskim diskom. Ta bo temeljil na dejstvu, da konformna preslikava na infinitezimalni ravni krožnice preslika v krožnice. Natančneje, predstavili bomo metodo polnjenja s krožnicami in z njeno pomočjo definirali zaporedje diskretnih preslikav, ki jih bomo zvezno razširili na triangulacijo obeh območij. Izkazalo se bo, da v limiti dobimo biholomorfno preslikavo iz Riemannovega upodobitvenega izreka.

Keywords

matematika;konformne preslikave;kvazikonformne preslikave;polnjenje s krožnicami;

Data

Language:	Slovenian
Year of publishing:	2018
Typology:	2.11 - Undergraduate Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[A. Kišek]
UDC:	517.5
COBISS:	18455641
Views:	709
Downloads:	228
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	The Discrete Interpretation of The Riemann Mapping Theorem
Secondary abstract:	In this thesis we will observe the Riemann mapping theorem in an alternative way through the theory of discrete analytic functions. The fact that conformal mapping sends infinitesimal circles to circles will be used to construct biholomorphism between non-empty simply connected open subset of the complex plane and the open unit disk. We will describe a method called circle packing, which will help us to define a sequence of discrete mappings which can be continuously extended to a triangulation of both domains. Finally, we will prove that this sequence converges to a conformal mapping, which conicides with the one from the Riemann mapping theorem.
Secondary keywords:	mathematics;conformal mappings;quasiconformal mappings;circle packing;
Type (COBISS):	Final seminar paper
Study programme:	0
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Matematika - 1. stopnja
Pages:	27 str.
ID:	10961995