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Finiteness of the number of ends of minimal submanifolds in Euclidean space
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8422-6140
1994 (English)In: Manuscripta mathematica, ISSN 0025-2611, E-ISSN 1432-1785, Vol. 82, p. 313-330Article in journal (Refereed) Published
Abstract [en]

We prove a version of the well-known Denjoy-Ahlfors theorem about the number of asymptotic values of an entire function for properly immersed minimal surfaces of arbitrary codimension in ℝN. The finiteness of the number of ends is proved for minimal submanifolds with finite projective volume. We show, as a corollary, that a minimal surface of codimensionn meeting anyn-plane passing through the origin in at mostk points has no morec(n, N)k ends.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 1994. Vol. 82, p. 313-330
Keywords [en]
Projective volume, ends, minimal submanifolds
National Category
Geometry Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-133949DOI: 10.1007/BF02567704OAI: oai:DiVA.org:liu-133949DiVA, id: diva2:1065704
Available from: 2017-01-16 Created: 2017-01-16 Last updated: 2017-11-29Bibliographically approved

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