Abstract/Details

Constant mean curvature cylinders


2000 2000

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Abstract (summary)

This thesis is concerned with the problem of constructing surfaces of constant mean curvature. More specifically, we are interested in obtaining immersions of the twice punctured Riemann sphere into three dimensional Euclidean space with constant mean curvature. Constant mean curvature surfaces can be described by a Weier-strass type representation, the DPW method, in terms of holomorphic loop Lie algebra valued 1-forms. For the construction of cylinders with the DPW method, the need arises to investigate holonomy problems and we derive explicit conditions on the holomorphic loop Lie algebra valued 1-forms which ensure periodicity of the resulting immersion. This allows us to construct three new families of constant mean curvature cylinders, each of which include surfaces that possess umbilic points. The first class consists of surfaces with a closed planar geodesic on which arbitrarily many umbilics may be positioned. In the second class each surface has a closed curve of points with a common tangent plane. The third class consists of cylinders with one end asymtotic to a Delaunay surface.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences, Constant mean curvature, Cylinders, Umbilic points
Title
Constant mean curvature cylinders
Author
Kilian, Martin Leon Peter
Number of pages
76
Publication year
2000
Degree date
2000
School code
0118
Source
DAI-B 61/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
9780599957466, 0599957468
Advisor
Pedit, Franz
University/institution
University of Massachusetts Amherst
University location
United States -- Massachusetts
Degree
Ph.D.
Source type
Dissertations & Theses
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9988809
ProQuest document ID
304606642
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
http://search.proquest.com/docview/304606642
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