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arXiv · 2507.12398

Two classification results for stationary surfaces of the least moment of inertia

Rafael López
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Abstract

A surface in Euclidean space $\r^3$ is said to be an $α$-stationary surface if it is a critical point of the energy $\int_Σ|p|^α$, where $α\in\r$. We prove that all ruled $α$-stationary surfaces are vector planes (for all $α$) and a type of elongated helicoids (for $α=1$). The second result of classification asserts that if $α\not=-2,-4$, any $α$-stationary surface foliated by circles must be a rotational surface. If $α=-4$, the surface is the inversion of a plane, a helicoid, a catenoid or an Riemann minimal example. If $α=-2$, we find many non-spherical cyclic $(-2)$-stationary surfaces.

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Rafael López. 2025-09-28. Two classification results for stationary surfaces of the least moment of inertia. https://arxiv.org/abs/2507.12398

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