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Riemann mapping theorem

Nina Potočar (2017) Riemann mapping theorem. Diploma thesis.

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    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.

    Item Type: Thesis (Diploma thesis)
    Keywords: holomorphic functions, linear fractional transformations, Schwarz lemma, Riemann mapping theorem
    Number of Pages: 21
    Language of Content: Slovenian
    Mentor / Comentors:
    Mentor / ComentorsIDFunction
    izr. prof. dr. Marko SlaparMentor
    Link to COBISS: http://www.cobiss.si/scripts/cobiss?command=search&base=50126&select=(ID=11694153)
    Institution: University of Ljubljana
    Department: Faculty of Education
    Item ID: 4651
    Date Deposited: 13 Sep 2017 09:18
    Last Modified: 13 Sep 2017 09:18
    URI: http://pefprints.pef.uni-lj.si/id/eprint/4651

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