On Liouville’s theorem for locally quasiregular mappings inR
n |
| |
Authors: | Peter Lindqvist |
| |
Institution: | (1) Institute of Mathematics, Helsinki University of Technology, SF-02150 Espoo 15, Finland |
| |
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. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|