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arXiv · 2610.38563

Prescribed mean curvature surfaces of Riemann minimal type

Antonio Bueno
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Abstract

We construct analogues of Riemann minimal examples among surfaces in the Euclidean 3-space whose mean curvature is given by a prescribed function on the unit sphere in terms of their Gauss map. Specifically, we obtain a 2-parameter family of complete, properly embedded surfaces foliated by circles and straight lines and invariant under a nontrivial translation.

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Antonio Bueno. 2026-10-28. Prescribed mean curvature surfaces of Riemann minimal type. https://arxiv.org/abs/2610.38563

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