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This is a Quantitative Study study.

October 19, 2025Open Access

Stationary surfaces for the moment of inertia with constant Gauss curvature

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Only planes and spheres are stationary surfaces for the defined energy functional.
The study shows that constant Gauss curvature uniquely characterizes these surfaces.
Assuming a principal curvature or mean curvature is constant leads to classification of these surfaces.
The energy functional integrates the norm of the shape’s tangent vectors with respect to the surface.

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Implication

This research identifies planes and spheres as stationary surfaces for moment of inertia, suggesting shapes with constant curvature are uniquely defined.

Cite This Study

Rafael López (2025) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc697013 https://doi.org/10.48550/arxiv.2507.12865

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Implication

This research identifies planes and spheres as stationary surfaces for moment of inertia, suggesting shapes with constant curvature are uniquely defined.

Stationary surfaces for the moment of inertia with constant Gauss curvature

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Implication

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Stationary surfaces for the moment of inertia with constant Gauss curvature

Key Points

Discussion

Implication

Cite This Study

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