@mismi,
Hard to keep a wavy line, one like soz's or a simple curve or two, when the ground cover is rambunctions.
I like ophiopogon (mondo) a lot myself - it worked well in my Venice garden. I used the mini one to good effect under some japanese maple trees. I also like a relative (if I remember correctly), Liriope... in small gardens in LA. Again, a lot of us don't know about your particular year round climate and its effect on rampantness of plants. LittleK has lived in Georgia and pays attention to plants..
I could rattle off a hundred(+) shade liking ground covers but I'm not going to.
I do hope you consult with some local experts, a very good local nursery (please don't only ask someone at home depot), professional garden designer with good repute, local arboretum, garden clubs (yea and nay on some of those), agricultural extension.
In Albuquerque, we have a book available at nurseries called Down to Earth, A Gardener's Guide to the Albuquerque Area. It's somewhere around $30.00.
I found it a good read when I first moved here, full of local advice, warnings, pros and cons, and source lists, with few things I'd argue about in a first look.