I don’t know what the technical term is - I mean, for example holding a weight in the up- part of a curl for as long as possible. Does that give any benefit in the area of building muscle?
I ask because for me it is slightly easier to discipline myself to do. I find it easier to hold a weight until my arm is desperate to drop, than to keep repeatedly lifting it until I can’t lift it again.
I know the latter is probably the better thing to do generally, but does the former (holding your muscles in a high-strain position) have any benefit towards muscle gain at all?
Isometric training. It’s useful in some situations, but should not be a mainstay of any program.
We used to do it a lot in kung fu - horse stance, iron body stance etc. It certainly correlated well with people’s strength, in that the toughest, strongest guys could maintain the stance for longest, but I couldn’t say if this was cause or effect. Iron body stance involved maintaining a low press-up position on your knuckles on a wooden floor for a protracted period of time. Mentally arduous as much as physically taxing. If you could take it, the Master would then come and stand on your back - you could try this with a friend 
It is written that when Wong Fei Hung sank into a horse stance, 10 strong men with poles could not move him. I didn’t get quite that far myself.
There’s probably a factual answer to your questions, so I’ll move the thread to GQ.
Isometric training does have it’s place in weight training - if done properly it can increase both strength and muscle size. Christian Thibedeau has an article on the subject down at the t-nation.com. http://www.t-nation.com/findArticle.do?article=313iso2 No one does only isometric training, though.
There was a recent thread about muscle soreness where someone linked an article about how such exercises (loading the muscle without moving it) cause more post-exercise soreness, but did not mention whether there was any benefit to doing it.