Work

Generalised convexity with respect to families of affine maps

Year: 2025

Type: article

Abstract: The standard closed convex hull of a set is defined as the intersection of all images, under the action of a group of rigid motions, of a half-space containing the given set. In this paper we propose a generalisation of this classical notion, that we call a (K, ℍ)-hull, and which is obtained from the above construction by replacing a half-space with some other closed convex subset K of the Euclidean space, and a group of rigid motions by a subset ℍ of the group of invertible affine transformations. The main focus is on the analysis of (K, ℍ)-convex hulls of random samples from K.

Source: Israel Journal of Mathematics

DOI: 10.1007/s11856-025-2751-0

Authors: Zakhar Kabluchko, Alexander Marynych, Ilya Molchanov

Institutions: University of Münster, Taras Shevchenko National University of Kyiv, University of Bern

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: University of Bern, National Research Foundation of Ukraine, National Research Foundation