works on
ball-convex bodies 1floating bodies 1illumination bodies 1isoperimetric inequality 1surface area measure 1

From the 1 of 4 linked papers with an AI index.

collaborators

4 papers

math.MG2026

Illumination bodies for ball-convex bodies

Brandon Oliva, Elisabeth M. Werner, Diliya Yalikun

The paper defines illumination and weighted illumination bodies for ‑ball convex sets, proves they are convex, introduces a relative surface‑area measure via a volume derivative…

math.MG2026

Illumination Bodies in Projective Geometries

Rotem Assouline, Florian Besau, Elisabeth M. Werner

We extend the notion of illumination bodies to Riemannian spaces of constant curvature and to projective Finsler geometries. We prove that the derivative of their volume defines a…

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…