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Two-point
functions and constant mean curvature surfaces in
$\mathbb{R}^3$
Peter McGrath and Everett Meekins |
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Vol. 16 (2023), No. 3, 467–482
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Abstract |
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Using a two-point maximum principle technique inspired by work of Brendle and Andrews and Li, we give a new proof of a special case of Alexandrov’s theorem: there are no embedded constant mean curvature tori in Euclidean three-space. |
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Keywords
constant mean curvature, Hopf, Alexandrov, differential
geometry, geometric analysis, surface
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Mathematical Subject Classification
Primary: 53A10
Secondary: 35J93
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Milestones
Received: 2 February 2022
Revised: 21 June 2022
Accepted: 25 June 2022
Published: 10 August 2023
Communicated by Michael Dorff
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Authors |
| Peter McGrath | |
| Department of Mathematics North Carolina State University Raleigh, NC United States |
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| Everett Meekins | |
| North Carolina State
University Raleigh, NC United States |
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| © 2023 MSP (Mathematical Sciences Publishers). |
