How do I use a convex crepe pan?
As far as I can tell what you don't do is pour the batter onto the pan.  What you do do is dip the warmed pan into batter (I'd think you stick just the cooking surface into the batter, not the whole thing) and put it back on your burner to cook a crepe quickly.

See the product description on this convex pan on amazon and this vintage pan on ebay for where I got my information.