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Riemannov upodobitveni izrek : diplomsko delo
Potočar, Nina (Author), Slapar, Marko (Mentor) More about this mentor... This link opens in a new window

URLURL - Presentation file, Visit http://pefprints.pef.uni-lj.si/id/eprint/4651 This link opens in a new window

Abstract
V prvem delu diplomske naloge najprej predstavimo osnovne definicije in lastnosti kompleksne ravnine. V nadaljevanju se osredotočimo na kompleksne funkcije in lomljene linearne transformacije. Eno izmed bolj pomembnih poglavij je tudi Schwarzova lema in avtomorfizmi kroga. V drugem delu predstavimo Riemannov upodobitveni izrek, ki nam pove, da je vsako enostavno povezano območje v ₵, razen cele kompleksne ravnine, biholomorfno ekvivalentno enotskemu disku. Nato razložimo, zakaj izrek ne velja za celotno kompleksno ravnino. Na koncu sledijo primeri uporabe Riemannovega upodobitvenega izreka.

Language:Slovenian
Keywords:holomorfne funkcije, lomljene linearne preslikave, Schwarzova lema, Riemannov upodobitveni izrek
Work type:Bachelor thesis/paper (mb11)
Tipology:2.11 - Undergraduate Thesis
Organization:PEF - Faculty of Education
Year:2017
Publisher:[N. Potočar]
Number of pages:IV, 21 str.
UDC:51(043.2)
COBISS.SI-ID:11694153 Link is opened in a new window
Views:318
Downloads:74
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Secondary language

Language:English
Title:Riemann mapping theorem
Abstract:
In the first part of the thesis, we introduce the basic definitions and properties of the complex plane. We then focus on complex functions and linear fractional transformations. One of the main chapters of the thesis is the one regarding the Schwarz lemma and the automorphisms of the unit disk. In the second part of the diploma thesis we present the Riemann mapping theorey, which states that every simply connected domain in ₵, except for the whole plane, is biholomorphically equivalent to the unit disc. We then explain why the theorey does not apply to the whole complex plane. The final part of the thesis contains examples of the Riemann mapping theorey.

Keywords:mathematics, matematika

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