Mappings of finite distortion on metric surfaces
Meier, D., & Rajala, K. (2024). Mappings of finite distortion on metric surfaces. Mathematische Annalen, Early online. https://doi.org/10.1007/s00208-024-02972-z
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Mathematische AnnalenDate
2024Copyright
© The Author(s) 2024
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.
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0025-5831Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/242602404
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