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Stable complete minimal surfaces in hyperkahler manifolds
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UNSPECIFIED (1998) Stable complete minimal surfaces in hyperkahler manifolds. COMPOSITIO MATHEMATICA, 112 (1). pp. 33-40. ISSN 0010-437X.
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Abstract
In this paper we prove that an isometric stable minimal immersion of a complete oriented surface into a hyperkahler 4-manifold is holomorphic with respect to an orthogonal complex structure, if it satisfies a Bernstein-type assumption on the Gauss-lift. This result generalizes a theorem of Micallef for minimal surfaces in the euclidean 4-space. An example found by Atiyah and Hitchin shows that the assumption on the Gauss-lift is necessary.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Journal or Publication Title: | COMPOSITIO MATHEMATICA | ||||
Publisher: | KLUWER ACADEMIC PUBL | ||||
ISSN: | 0010-437X | ||||
Official Date: | May 1998 | ||||
Dates: |
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Volume: | 112 | ||||
Number: | 1 | ||||
Number of Pages: | 8 | ||||
Page Range: | pp. 33-40 | ||||
Publication Status: | Published |
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