Work

Stability of reverse isoperimetric inequalities in the plane: Area, Cheeger, and inradius

Year: 2026

Type: article

Abstract: In this paper, we present stability results for various reverse isoperimetric problems in . Specifically, we prove the stability of the reverse isoperimetric inequality for ‐convex bodies — convex bodies with the property that each of their boundary points supports a ball of radius so that the body lies inside the ball in a neighborhood of . For convex bodies with smooth boundaries, ‐convexity is equivalent to having the curvature of the boundary bounded below by . Additionally, within this class of convex bodies, we establish stability for the reverse inradius inequality and the reverse Cheeger inequality. Even without its stability version, the sharp reverse Cheeger inequality is new in dimension 2.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70292

Authors: Kostiantyn Drach, Kateryna Tatarko

Institutions: Centre de Recerca Matemàtica, Universitat de Barcelona, University of Waterloo

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Generalitat de Catalunya, Natural Sciences and Engineering Research Council of Canada, Agencia Estatal de Investigación