Somehow Topcoder Arena does not work in chrome or firefox browsers in Ubuntu 11.10.
This is what you can do instead:
(1) Download http://www.topcoder.com/contest/classes/ContestApplet.jar to your local directory.
(2) Run the following code in a terminal.
java -cp ContestApplet.jar com.topcoder.client.contestApplet.runner.generic www.topcoder.com 5001
This method works in openjdk as well.
Update: this seems no longer working for Java 7. The ultimate solution is to configure Ubuntu/Mac etc. to open .jnlp files with javaws, similar to the instructions in this post.