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Denjoy-Ahlfors theorem for harmonic functions on Riemannian manifolds and external structure of minimal surfaces
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8422-6140
Volgograd State University, Russia.
1996 (English)In: Communications in analysis and geometry, ISSN 1019-8385, E-ISSN 1944-9992, Vol. 4, no 4, p. 547-587Article in journal (Refereed) Published
Abstract [en]

We extend the well-known Denjoy-Ahlfors theorem about the number of different asymptotic tracts of a holomorphic function to subharmonic functions on arbitrary Riemannian manifolds. We obtain some versions of the Liouville theorem for Aa-harmonic functions without the geodesic completeness requirement on a manifold. Moreover, the upper estimate of the topological index of the height function of a minimal surface in Rn has been established and, as a consequence, a new prove of the Bernstein's theorem has been derived. Other applications to the theory of minimal surfaces are also discussed.

Place, publisher, year, edition, pages
International Press of Boston , 1996. Vol. 4, no 4, p. 547-587
Keywords [en]
Denjoy-Ahlfors theorem, harmonic functions, Riemannian manifolds, minimal surfaces
National Category
Mathematical Analysis Geometry
Identifiers
URN: urn:nbn:se:liu:diva-133944DOI: 10.4310/CAG.1996.v4.n4.a2OAI: oai:DiVA.org:liu-133944DiVA, id: diva2:1065666
Available from: 2017-01-16 Created: 2017-01-16 Last updated: 2017-11-29Bibliographically approved

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Publisher's full texthttp://www.intlpress.com/site/pub/pages/journals/items/cag/content/vols/0004/0004/a002/

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