proof of Liouville’s theorem
where is the circle of radius about , for . Then can be estimated as
where .
But is bounded, so there is such that for all . Then for all and all . But since is arbitrary, this gives whenever . So for all , so is constant.
Title | proof of Liouville’s theorem |
---|---|
Canonical name | ProofOfLiouvillesTheorem |
Date of creation | 2013-03-22 12:54:15 |
Last modified on | 2013-03-22 12:54:15 |
Owner | Evandar (27) |
Last modified by | Evandar (27) |
Numerical id | 5 |
Author | Evandar (27) |
Entry type | Proof |
Classification | msc 30D20 |