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Constant mean curvature surfaces in hyperbolic 3-space
Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy.
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

The aim of this bachelor's thesis has been to investigate surfaces that are the main contributions to scattering amplitudes in a type of string theory. These are constant mean curvature surfaces in hyperbolic 3-space. Classically the way to find such surfaces has been to solve a non-linear partial differential equation. In many spaces constant mean curvature surfaces are intimately connected to certain harmonic maps, known as the Gauss maps. In 1995 Dorfmeister, Pedit, and Wu established a method for constructing harmonic maps into so-called symmetric spaces. I investigate a generalization of this method that can be applied to find constant mean curvature surfaces in hyperbolic 3-space by using the intimate connection between these surfaces and harmonic maps. This method relies on a factorization of a Lie-group valued map. I show an explicit method for finding the factorization in terms of what is known as the Birkhoff factorization. Because approximation methods for the Birkhoff factorization are known, this allowed me to use the method constructively to find constant mean curvature surfaces in hyperbolic 3-space.

Place, publisher, year, edition, pages
2014. , 36 p.
Series
FYSAST, FYSKAND1010
Keyword [en]
String theory, hyperbolic 3-space, DPW-method
National Category
Other Physics Topics
Identifiers
URN: urn:nbn:se:uu:diva-225923OAI: oai:DiVA.org:uu-225923DiVA: diva2:722890
Educational program
Bachelor Programme in Physics
Supervisors
Examiners
Available from: 2014-06-24 Created: 2014-06-09 Last updated: 2014-06-24Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • 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
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