Work

On Generalized Disc-Polygons in Plane Convex Bodies With a Higher Degree of Smoothness

Year: 2026

Type: article

Abstract: We prove power series expansions for the expectations of the number of vertices and missed area of random L -convex polygons in planar convex bodies with sufficiently smooth boundaries. Random L -convex polygons arise as the intersection of all translates of a fixed convex set L that contain i.i.d. uniform random points from a suitable plane convex body K . Our results extend the asymptotic formulas proved in Fodor, Papvári and Vígh [11] and Fodor and Montenegro [9], and have consequences about L -convex floating bodies and relative affine surface area that were investigated by Schütt, Werner and Yalikun in [19].

Source: Results in Mathematics

DOI: 10.1007/s00025-026-02760-y

Authors: Ferenc Fodor, Dániel I. Papvári

Institution: University of Szeged

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, Szegedi Tudományegyetem, Nemzeti Kutatási, Fejlesztési és Innovaciós Alap