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On the Gauss map of embedded minimal tubes
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8422-6140
Volgograd State University.
1999 (English)In: Note di Matematica, ISSN 1123-2536, E-ISSN 1590-0932, Vol. 19, no 1, p. 7-17Article in journal (Refereed) Published
Abstract [en]

A surface is called a tube if its level-sets with respect to some coordinate function (the axis of the surface) are compact. Any tube of zero mean curvature has an invariant, the so-called flow vector. We study how the geometry of the Gaussian image of a higher-dimensional minimal tube M is controlled by the angle alpha(M) between the axis and the flow vector of M. We prove that the diameter of the Gauss image of M is at least 2alpha(M). As a consequence we derive an estimate on the length of a two-dimensional minimal tube M in terms of alpha(\M) and the total Gaussian curvature of M.

Place, publisher, year, edition, pages
University of Salento: SIBA , 1999. Vol. 19, no 1, p. 7-17
Keyword [en]
Minimal surfaces, Gauss map, embedded
National Category
Geometry Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-133936OAI: oai:DiVA.org:liu-133936DiVA, id: diva2:1065629
Available from: 2017-01-16 Created: 2017-01-16 Last updated: 2017-11-29Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • vancouver
  • Other style
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  • de-DE
  • en-GB
  • en-US
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  • nn-NO
  • nn-NB
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  • Other locale
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