Work

An interpolation of metrics and spaces of metrics

Year: 2026

Type: article

Abstract: As a generalization of Hausdorff's extension theorem of metrics, we prove an interpolation theorem of a family of metrics defined on closed subsets of metrizable spaces. As an application, we investigate typicality of subsets of moduli spaces of metrics. We observe that various sets of all metrics with properties appearing in metric geometry are dense intersections of countably many open subsets in spaces of metrics on metrizable spaces. For instance, our study is applicable to the set of all non-doubling metrics and the set of all non-uniformly disconnected metrics.

Source: Topology and its Applications

DOI: 10.1016/j.topol.2026.109856

Author: Yoshito Ishiki

Institution: Tokyo Metropolitan University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,920

Funders: Tokyo Metropolitan University, Japan Society for the Promotion of Science