arXiv subjects

Diliya Yalikun

Publications and source records attributed to Diliya Yalikun.

3 recordsLinked to original sources

arXiv2026

Illumination bodies for ball-convex bodies

We introduce illumination bodies and weighted illumination bodies in the class of $n$-dimensional $R$-ball convex bodies. These bodies may be regarded as dual counterparts of the recently introduced $R$-ball floating bodies. We prove that the illumination bodies are convex. We also show that a left derivative of volume gives rise to a surface area measure for ball-convex bodies, the relative surface area measure. In dimension $2$, we establish an isoperimetric inequality for this relative surface area.

math.MG↗

arXiv2025

Ball-convex bodies and $L_p$ relative surface areas

We define new surface area measures for ball-convex bodies which we call $L_p$ relative surface areas. We show that those are rigid motion invariant valuations. We establish inequalities for these quantities and prove a monotonicity behavior which leads to a new notion of entropy for ball-convex bodies. We introduce a weighted ball floating body. A derivative of volume of a ball-convex body with a weighted ball floating body provides a geometric interpretation of the $L_p$ relative surface areas.

math.MG↗

arXiv2025

Floating bodies for ball-convex bodies

We define floating bodies in the class of $n$-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 semi continuous valuation.

math.MG↗