Is there a culinary term describing "frying in about 4mm of water" in a frying pan without oil (with this technique, if water evaporates you just keep adding more from a glass, keeping it shallow). 
I disagree with Neil's answer here. All the three terms of "poaching", "boiling" or "simmering" require that your food is fully submerged, especially for poaching it has to be free-floating in a large amount of water. I doubt that you are submerging anything in 4 mm, and this little amount of water would boil off quickly if you had so little food that it is submerged.   Depending on the exact circumstances and the type of food (veggies vs grains vs meat), but also on the size of the food chunks, what you are doing is either sweating, steaming or braising, but in a very inefficient form.   Sweating would be part of the initial browning of vegetables before further use in a soup or similar, until they are softer. It usually involves some browning, but this won't happen when you are using water. In fact, you're better off leaving the water out altogether in this case and use either fat or nothing.   Steaming can be done with vegetables or grains. It is better done with somewhat more water than you describe, but still much less than needed for boiling them. The "mix food and water in the pan/pot" technique is better suited for grains, vegetables do better in a steamer suspended over a large amount of boiling water, without touching the water.   Braising is normally used for meat, but can also be done with other food which can be cut up in largish chunks (aubergines would do, but not peas, for example). It is tastier when done in a sauce than in water.   Unlike shallow frying, which is done with oil, what you are doing does not have a name of its own, because it is not something usually done when cooking. Depending on what you are trying to do, there are better ways to go about it.  