Floating bodies for ball-convex bodies

Key Points

• The study defines floating bodies within the framework of ball-convex bodies, expanding geometric understanding.
• It introduces relative affine surface area as a measure derived from the volume of floating bodies, highlighting its geometric significance.
• This relative affine surface area is shown to be upper semi continuous and invariant under rigid motions, indicating its robustness.
• Geometric properties of these bodies provide essential insights into the relationship between volume and surface area in higher dimensions.