Thanks for joining the forum ... hope you are enjoying the book!
I knew that this question - sharpening u-gouges - which I completely ignored in the book, would come up pretty soon!
Although they
can be sharpened on a normal flat stone, by carefully rocking them back and forth while rubbing along the surface, it is of course much easier if you have a stone with a groove that matches the radius of the blade. Instructions on how to make such a stone yourself - a surprisingly easy job - are on a page of my site
here.
As for the inner edge of the blade, you can make a rounded stone for this yourself (instructions for this are on that page too), but it is also possible to use the 'low-tech' solution of using a very delicate piece of sandpaper wrapped around a pencil. This works fine, especially if the sandpaper is a particularly worn piece.