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December 1, 2025Journal of the London Mathematical Society4 citations

Floating bodies for ball‐convex bodies

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CSCarsten SchüttEWElisabeth M. WernerDYDiliya Yalikun

Key Points

  • 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.

Abstract

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. (2025) studied this question.

synapsesocial.com/papers/69402a7e2d562116f29021aahttps://doi.org/10.1112/jlms.70387
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Convex Functions: Constructions, Characterizations and Counterexamples2009 · 223 citations
  2. 2Random points on the boundary of smooth convex bodies2002 · 57 citations
  3. 3The Bernstein problem for affine maximal hypersurfaces2000 · 149 citations
  4. 4Isometries of the class of ball-bodies2025 · 3 citations
  5. 5The convex floating body.1990 · 158 citations