Bäcklund transformations for minimal surfaces
Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
In this thesis, we study a Bäcklund transformation for minimal surfaces - surfaces with vanishing mean curvature - transforming a given minimal surface into a possible infinity of new ones.
The transformation, also carrying with it mappings between solutions to the elliptic Liouville equation, is first derived by using geometrical concepts, and then by using algebraic methods alone - the latter we have not been able to find elsewhere. We end by exploiting the transformation in an example, transforming the catenoid into a family of new minimal surfaces.
Place, publisher, year, edition, pages
2015. , 53 p.
Bäcklund transformations, Liouville equation, minimal surfaces, Ribaucour transformations, Thybaut transformations.
IdentifiersURN: urn:nbn:se:liu:diva-119914ISRN: LiTH-MAT-EX--2015/04--SEOAI: oai:DiVA.org:liu-119914DiVA: diva2:833320
Subject / course