On Liouville’s theorem for locally quasiregular mappings inR
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| Authors: | Peter Lindqvist |
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| Institution: | (1) Institute of Mathematics, Helsinki University of Technology, SF-02150 Espoo 15, Finland |
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| Abstract: | Letf:R
n→Rn be locally quasiregular in the sense that the restriction off to any ball |x|<r has finite inner dilatationK
1(r). Suppose that the growth condition ∫∞r-1K1(r)1/(1-n) holds. Then Liouville’s theorem is valid:If f is bounded, f is a constant. An example shows that this growth condition is relatively sharp. |
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