December 1, 2025

Floating bodies for ball‐convex bodies

Puntos clave

Upper semicontinuous valuation characterizes the relative affine surface area of floating bodies in ball-convexity.
The concept of floating bodies integrates geometric properties with right derivatives of volume in mathematical forms.
Rigid motion invariance is a key aspect of defining surface area measures for this class of geometric bodies.
Insights into floating bodies may pave the way for further exploration in geometric valuations and novel applications.

Resumen

Abstract We define floating bodies in the class of ‐dimensional ball‐convex bodies. A right derivative of volume of these floating bodies leads to a surface area measure for ball‐convex bodies which we call relative affine surface area. We show that this quantity is a rigid motion invariant, upper semicontinuous valuation.

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Cite This Study

Schütt et al. (Mon,) studied this question.

synapsesocial.com/papers/69402a7e2d562116f29021aa https://doi.org/https://doi.org/10.1112/jlms.70387

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