MINIMAL GRAPHS WITH PLANAR ENDS

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Published: May 15, 2011
DOI: https://doi.org/10.14403/jcms.2011.24.2.313
Keywords:
minimal graphs, planar ends, torques, Harmonic function
Mathematics Subject Classification (2020):
Primary 53A10

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Sun Sook Jin
Department of Mathematics Education, Gongju National University of Education

Abstract





In this article, we consider an unbounded minimal graph M ⊂ R3 which is contained in a slab. Assume that ∂M consists of two Jordan curves lying in parallel planes, which is symmetric with the reflection under a plane. If the asymptotic behavior of M is also symmetric in some sense, then we prove that the minimal graph is itself symmetric along the same plane.





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Article Details

Issue
Vol. 24 No. 2 (2011)
Section
Articles