3 papers
math.MG2026
Illumination bodies for ball-convex bodies
Brandon Oliva, Elisabeth M. Werner, Diliya Yalikun
We introduce illumination bodies and weighted illumination bodies in the class of -dimensional -ball convex bodies. These bodies may be regarded as dual counterparts of the r…
math.MG2025
Ball-convex bodies and relative surface areas
Elisabeth M. Werner, Diliya Yalikun
We define new surface area measures for ball-convex bodies which we call relative surface areas. We show that those are rigid motion invariant valuations. We establish inequa…
math.MG2025
Floating bodies for ball-convex bodies
Carsten Schuett, Elisabeth M Werner, Diliya Yalikun
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…