The Uniformization Theorem
(2021) In Bachelor's Theses in Mathematical Sciences MATK11 20211Mathematics (Faculty of Engineering)
Mathematics (Faculty of Sciences)
- Abstract
- In this bachelor's thesis we provide a self contained proof of the Uniformization Theorem. It states that a simply connected Riemann surface is conformally equivalent to either the complex plane C, the unit disk D, or the Riemann sphere C^*. The proof given in this thesis is purely analytic and is based on the construction of Green's function and bipolar Green's function of a Riemann surface through the Perron method.
- Popular Abstract (Swedish)
- En myra som lever på en sfär kan förflytta sig i två dimensioner, framlänges och i sidled. Utan några kunskaper om den globala topologin av myrans värld, så kan den inte urskilja om den lever på en sfär eller i det tvådimensionella talplanet. På ett liknande sätt kan man inom matematiken formalisera en abstrakt topologisk yta som lokalt har samma egenskaper som det komplexa talplanet: En så kallad Riemannyta. Dessa ytor är viktiga objekt inom komplex analys och de används för att studera analytiska funktioner. I detta verk presenteras ett bevis för en känd sats som i stora drag säger att en Riemannyta utan ``hål'' antingen måste vara det komplexa talplanet, en cirkular skiva eller en sfär.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9045229
- author
- Zozoulenko, Nikita LU
- supervisor
- organization
- course
- MATK11 20211
- year
- 2021
- type
- M2 - Bachelor Degree
- subject
- keywords
- complex analysis, riemann surface, analytic functions, holomorphic functions, differential geometry, harmonic, subharmonic, perron, analysis
- publication/series
- Bachelor's Theses in Mathematical Sciences
- report number
- LUNFMA-4110-2021
- ISSN
- 1654-6229
- other publication id
- 2021:K13
- language
- English
- id
- 9045229
- date added to LUP
- 2022-08-08 17:43:39
- date last changed
- 2022-08-08 17:43:39
@misc{9045229, abstract = {{In this bachelor's thesis we provide a self contained proof of the Uniformization Theorem. It states that a simply connected Riemann surface is conformally equivalent to either the complex plane C, the unit disk D, or the Riemann sphere C^*. The proof given in this thesis is purely analytic and is based on the construction of Green's function and bipolar Green's function of a Riemann surface through the Perron method.}}, author = {{Zozoulenko, Nikita}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor's Theses in Mathematical Sciences}}, title = {{The Uniformization Theorem}}, year = {{2021}}, }