If you cut them down, as has been said, you will eventually kill them
if you keep cutting the tops off because they need leaves to
photosynthesize. This produces the carbohydrates (CHO = food) for the
rest of the plant so you will eventually starve them to death if you
keep the leaves cut off. In the mean time, they will live and
resprout from stored CHO's until they are depleted and then the plant
dies. As was said, that may take a while but, if you're willing to
stick with it and don't wait until the sprouts get big, it will work.
If you ring the tree, you'll just cause it to sprout more.
Herbicides sprayed on the foliage (Rodeo is the aquatic version of
Roundup since it's over a pond) will work.
Depending on their size, it might be hard to get the foliage sprayed.