Mappings of finite distortion on metric surfaces
DOKPE
- Meier, Damaris ORCID University of Fribourg
- Rajala, Kai University of Jyväskylä, Finland
- 2024
Published in:
- Mathematische Annalen. - London, UK : Springer Nature. - 2024, p. 1-29
English
We investigate basic properties of mappings of finite distortion f : X → R2, where
X is any metric surface, i.e., metric space homeomorphic to a planar domain with
locally finite 2-dimensional Hausdorff measure.We introduce lower gradients, which
complement the upper gradients of Heinonen and Koskela, to study the distortion of
non-homeomorphic maps on metric spaces. We extend the Iwaniec-Šverák theorem
to metric surfaces: a non-constant f : X → R2 with locally square integrable upper
gradient and locally integrable distortion is continuous, open and discrete. We also
extend the Hencl-Koskela theorem by showing that if f is moreover injective then
f −1 is a Sobolev map.
Mathematics Subject Classification Primary 30L10 · 30C65; Secondary 30F10
X is any metric surface, i.e., metric space homeomorphic to a planar domain with
locally finite 2-dimensional Hausdorff measure.We introduce lower gradients, which
complement the upper gradients of Heinonen and Koskela, to study the distortion of
non-homeomorphic maps on metric spaces. We extend the Iwaniec-Šverák theorem
to metric surfaces: a non-constant f : X → R2 with locally square integrable upper
gradient and locally integrable distortion is continuous, open and discrete. We also
extend the Hencl-Koskela theorem by showing that if f is moreover injective then
f −1 is a Sobolev map.
Mathematics Subject Classification Primary 30L10 · 30C65; Secondary 30F10
- Faculty
- Faculté des sciences et de médecine
- Department
- Département de Mathématiques
- Language
-
- English
- Classification
- Mathematics
- License
- CC BY
- Open access status
- hybrid
- Identifiers
-
- DOI 10.1007/s00208-024-02972-z
- ISSN 0025-5831
- ISSN 1432-1807
- Persistent URL
- https://folia.unifr.ch/unifr/documents/329262
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