Work

Poincaré inequality and energy of separating sets

Year: 2025

Type: article

Abstract: We study geometric characterizations of the Poincaré inequality in doubling metric measure spaces in terms of properties of separating sets. Given a couple of points and a set separating them, such properties are formulated in terms of several possible notions of energy of the boundary, involving for instance the perimeter, codimension type Hausdorff measures, capacity, Minkowski content and approximate modulus of suitable families of curves. We prove the equivalence within each of these conditions and the 1-Poincaré inequality.

Source: Advances in Calculus of Variations

DOI: 10.1515/acv-2024-0109

Authors: Emanuele Caputo, Nicola Cavallucci

Institutions: University of Warwick, École Polytechnique Fédérale de Lausanne

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: European Research Council

Award: G8280846135