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The Open Mapping Theorem for Analytic Functions and some applications
Karlstad University, Faculty of Technology and Science.
2006 (English)Independent thesis Advanced level (degree of Magister), 20 points / 30 hpStudent thesis
Abstract [en]

This thesis deals with the Open Mapping Theorem for analytic functions on domains in the complex plane: A non-constant analytic function on an open subset of the complex plane is an open map.

As applications of this fundamental theorem we study Schwarz’s Lemma and its consequences concerning the groups of conformal automorphisms of the unit disk and of the upper halfplane.

In the last part of the thesis we indicate the first steps in hyperbolic geometry.

Abstract [sv]

Denna uppsats behandlar satsen om öppna avbildningar för analytiska funktioner på domäner i det komplexa talplanet: En icke-konstant analytisk funktion på en öppen delmängd av det komplexa talplanet är en öppen avbildning.

Som tillämpningar på denna fundamentala sats studeras Schwarz’s lemma och dess konsekvenser för grupperna av konforma automorfismer på enhetsdisken och på det övre halvplanet.

I uppsatsens sista del antyds de första stegen inom hyperbolisk geometri.

Place, publisher, year, edition, pages
2006. , p. 30
Keywords [en]
open mapping theorem, maximum modulus principle, maximum modulus theorem, Schwarz's lemma, Poincaré's half-plane model, conformal group, conformal representation, hyperbolic distance
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kau:diva-210OAI: oai:DiVA.org:kau-210DiVA, id: diva2:5852
Presentation
2006-05-23
Uppsok
fysik/kemi/matematik
Supervisors
Examiners
Available from: 2006-06-21 Created: 2006-06-21

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf