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September 19, 2025Analysis

Stationary surfaces for the moment of inertia with constant Gauss curvature

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Only planes and spheres serve as stationary surfaces for the moment of inertia under constant Gauss curvature.
The primary finding indicates a unique relationship between the surfaces and their curvature properties.
Energy defined by the moment of inertia integral is proven to only stabilize for specific surface shapes.
Characterization involves conditions where either principal curvature or mean curvature remains constant.

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Analysis reveals that only planes and spheres are stationary surfaces for moment of inertia, suggesting unique curvature properties.

Rafael López (2025) studied this question.

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