Unstable minimal surfaces and Heegaard splittings (Q1124173)
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scientific article; zbMATH DE number 4111604
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unstable minimal surfaces and Heegaard splittings |
scientific article; zbMATH DE number 4111604 |
Statements
Unstable minimal surfaces and Heegaard splittings (English)
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1989
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This paper refines a result of \textit{J. T. Pitts} and \textit{J. H. Rubinstein} on the existence of an unstable minimal surface obtained from a Heegaard surface for a 3-manifold by a minimax process [Proc. Cent. Math. Anal. Aust. Natl. Univ. 10, 163-176 (1986; Zbl 0602.49028)], and then uses this to prove that the 3-torus has a unique genus three Heegaard splitting and to give an example of a genus four minimal surface in the 3-torus.
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existence of an unstable minimal surface
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Heegaard surface for a 3- manifold
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3-torus
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genus three Heegaard splitting
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genus four minimal surface in the 3-torus
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