Definitions of Quasiconformality on Metric Surfaces
DOKPE
- Meier, Damaris ORCID University of Fribourg
- Rajala, Kai University of Jyväskylä
- 2025
Published in:
- Potential Analysis. - Springer Science and Business Media LLC. - 2025
Quasiconformal maps
Quasiregular maps
Mappings of finite distortion
Metric surface
Uniformization
Upper gradient
English
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.
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.
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
-
- English
- Classification
- Mathematics
- Other electronic version
- License
- CC BY
- Open access status
- hybrid
- Identifiers
-
- DOI 10.1007/s11118-025-10230-3
- ISSN 0926-2601
- Persistent URL
- https://folia.unifr.ch/unifr/documents/332218
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