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Möbius and Loewner energy on curves with corners
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2023 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Möbius- och Loewnerenergi av kurvor med hörn (Swedish)
Abstract [en]

The Möbius energy and the Loewner energy are two Möbius invariant quantaties defined for Jordan curves. We start by introducing some of the basic properties of these two energies. Both are finite if and only if the curves belong to a class called Weil-Petersson. The Weil-Petersson class does not contain curves with corners. In part motivated by recent work of Johansson and Viklund we introduce regularized versions of both the Mövius and Loewner energy which allow for certain curves with isolated corners. We also look at the derivative of the Loewner energy.

Abstract [sv]

Möbiusenergin och Loewnerenergin är två Möbius-invarianta kvantiteter definerade  för Jordan-kurvor. Vi börjar med att presentera några av de grundläggande egenskaperna hos dessa två energier. Båda är ändliga om och endast om kurvorna tillhör en klass som heter Weil-Petersson. Weil-Petersson-klassen innehåller inte kurvor med hörn. Delvis motiverad av nytt arbete av Johansson och Viklund introducerar vi regulariserade versioner av både Möbius- och Loewnerenergin som tillåter vissa kurvor med isolerade hörn. Vi tittar också på derivatan av Loewnerenergin.

Place, publisher, year, edition, pages
2023. , p. 28
Series
TRITA-SCI-GRU ; 2023:403
Keywords [en]
Loewner Energy, Möbius Energy
National Category
Other Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-346700OAI: oai:DiVA.org:kth-346700DiVA, id: diva2:1859952
Subject / course
Mathematics
Educational program
Master of Science - Mathematics
Supervisors
Examiners
Available from: 2024-05-23 Created: 2024-05-23 Last updated: 2024-05-23Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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  • de-DE
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  • en-US
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  • nn-NB
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  • Other locale
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Output format
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