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Minimal tubes of finite integral curvature
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8422-6140
1998 (English)In: Siberian mathematical journal, ISSN 0037-4466, E-ISSN 1573-9260, Vol. 39, no 1, p. 159-167Article in journal (Refereed) Published
Abstract [en]

The author defines a tube to be an immersed submanifold u:Mp→Rn+1 and the interval of existence τ(Mp) to be the interval of those t for which the intersection Σt of u(Mp) with the hyperplane xn+1=t in Rn+1 is nonempty and compact. The length of τ(Mp) is called the time of existence of the tube. The tube is minimal if u is a minimal immersion. Denote by vT an orthogonal projection of v into the tangent space of M, ν=eTn+1/∥eTn+1∥, and introduce a vector J, called a vector-flow with coordinates, Jk=∫Σt((ek)T,ν),1≤k≤n+1. The angle between J and en+1 is denoted by α. The main result of the article under review is the following estimate: |τ(M)|≤G(M)∥J∥cos(α)16α2, where G(M) denotes the absolute integral Gauss curvature of M.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 1998. Vol. 39, no 1, p. 159-167
Keywords [en]
Minimal surface, Gauss map, univalent functions, quasiconformal maps
National Category
Geometry Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-133938DOI: 10.1007/BF02732370OAI: oai:DiVA.org:liu-133938DiVA, id: diva2:1065638
Available from: 2017-01-16 Created: 2017-01-16 Last updated: 2017-11-29Bibliographically approved

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