Work

On the minimizer of the barycentric isoperimetric ratio among connected planar sets

Year: 2026

Type: preprint

Abstract: Among connected, planar sets, the ratio between the isoperimetric deficit and the squared barycentric asymmetry is known to be bounded from below by a strictly positive constant (as proved in recent papers by Bianchini-Croce-Henrot and Gambicchia-Pratelli). This opens the natural question whether the infimum is attained at some set. In this paper, we prove that a minimizer for this ratio actually exists, and moreover it is simply connected.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.15088

Authors: Gambicchia, Chiara, Pratelli, Aldo, Torres-Latorre, Clara

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni, Agencia Estatal de Investigación

Awards: G1549693833, G1908868068, G2971504390, G3435027008, G3693695517, G5044744888, G5153289039, G5195188938, G5642993642, G6893394547, G8097609347

OpenAlex ID: W7221770015

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