Ar. and Ric,
You guys are Asian dissent? That is Awesome........(no, I am a Caucasian but attended ASU in Jonesboro, Arkansas....home of the Red Wolf where the campus is predominant Middle Eastern, Asian, some Spanish, and Caucasian.)
Anyway, I have seen grass grow under large mature oak trees. The trick is to raise that canopy and clear obstructions in all corners to speed sunlight penetration. The ASU campus has fully matured oaks, pecan, cherry............all major Arkansas native trees for the Horticultural Department to educate with. There is Zoysia grasses growing under them. Where all else fails, there is fescues where the irrigation reaches.
Just food for thought..........in normal residential settings, without automatic irrigation, the attempt to establish turfgrass is futile. Im my short lived attempts to earn a decent grade in Ag. the thing to consider is the pH, the soil tilth, the nutrient deficiencies that appear around trees as a result of their massive wicking action and nutrient depletion. I find it too troublesome to compete with trees and grass in the same space. I often resort to the Southern Hillbilly anecdote of hunting---" Does grass grow under trees in the forest?" The answer is no-----too much light reduction, and over grown canopies to compete for light. Often some species of trees emit a toxin to control undergrowth and competing species of trees from growing. To me it no different that grass is in competition. If someone has a big pocket book with money falling out of it.............then go for it!!