How can I install crown cornice molding and trim on rounded outside corners?
You can add a center section at the corner that runs at a 45° angle to either wall. That cuts down on any gap you might have, but makes the installation and cutting a bit more difficult. My house has a few faux pillars that use this technique:



(I know, I know, I haven't gotten around to touch ups after we painted the walls...)

And here's a lookup table for cutting crown molding (source):