Apparently Liouville's theorem for conformal mappings holds for functions in $W^{1,n}$. Am I to understand that potentially, there are everywhere differentiable functions to which it doesn't apply?
2026-03-28 01:12:49.1774660369
Liouville's theorem for conformal mappings: differentiable functions?
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Any conformal differentiable map $f \colon \Omega \subseteq \mathbb R^n \to \mathbb R^n$ is automatically $W_\text{loc}^{1,n}$: see https://mathoverflow.net/questions/351088/regularity-of-conformal-maps