Meier, Damaris Rajala, Kai 2025 We explore the interplay between different definitions of distortion for mappings f : X → R2, where X is any metric surface, meaning that X is homeomorphic to a domain in R2 and has locally finite 2-dimensional Hausdorff measure. We establish that finite distortion in terms of the familiar analytic definition always implies finite distortion in terms of maximal and minimal stretchings along paths. The converse holds for maps with locally integrable distortion. In particular, we prove the equivalence of various notions of quasiconformality, implying a novel uniformization result for metric surfaces. application/pdf https://folia.unifr.ch/global/documents/332218 https://folia.unifr.ch/documents/332218/files/meier-rajala_definitions-of-quasiconformality_0.pdf eng https://link.springer.com/article/10.1007/s11118-025-10230-3 info:eu-repo/semantics/altIdentifier/doi/10.1007/s11118-025-10230-3 info:eu-repo/semantics/altIdentifier/issn/0926-2601 info:eu-repo/semantics/openAccess CC BY Potential Analysis. - Springer Science and Business Media LLC. - 2025 Quasiconformal maps Quasiregular maps Mappings of finite distortion Metric surface Uniformization Upper gradient info:eu-repo/classification/udc/51 Definitions of Quasiconformality on Metric Surfaces http://purl.org/coar/resource_type/c_6501