Puncture repair on metric measure spaces

TL;DR

This paper explores the concept of puncture repair within the context of quasiconformal mappings on metric measure spaces, extending ideas from conformal geometry and discussing the removability of porous sets.

Contribution

It generalizes puncture repair techniques from Riemannian manifolds to metric measure spaces and provides insights into the removability of porous sets in this setting.

Findings

Extension of puncture repair to metric measure spaces

Outline of removability criteria for porous sets

Connections between conformal geometry and quasiconformal mappings

Abstract

Motivated by recent interest concerning "puncture repair" in the conformal geometry of compact Riemannian manifolds, a brief exposition on generalisation to the setting of quasiconformal mappings on certain metric measure spaces is presented as well as a brief outline on removability of porous sets.