Biharmonic rotational surfaces in the four-dimensional Euclidean space are minimal
Differential Geometry
2026-05-18 v2
Abstract
In this paper, we show that any biharmonic simple rotational surface in the four-dimensional Euclidean space is minimal. The proof is based on reducing the biharmonic equation to a system of ordinary differential equations for the profile curve and then excluding all possible non-minimal branches. This is a partial affirmative answer to Chen's conjecture.
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Cite
@article{arxiv.2605.09587,
title = {Biharmonic rotational surfaces in the four-dimensional Euclidean space are minimal},
author = {Shun Maeta},
journal= {arXiv preprint arXiv:2605.09587},
year = {2026}
}
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16 pages