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arXiv · 2605.09587

Biharmonic rotational surfaces in the four-dimensional Euclidean space are minimal

Shun Maeta
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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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Shun Maeta. 2026-05-10. Biharmonic rotational surfaces in the four-dimensional Euclidean space are minimal. https://arxiv.org/abs/2605.09587

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