Like most technologists who frequent this site, I'm all for following the scientific method and gathering data through repeatable experiments that test hypotheses, and I'm against petty tradition ("we've always done it this way" is a very counterproductive/backwards way of thinking that also precludes progress -- as an entrepreneurial community, we tend to think differently and to challenge established beliefs here on HN).
I'd be very interested in reading them.
Nevertheless, I will still provide you with some samples of evidence (these are high level summaries but actual studies are linked within:
Meditation:
https://en.m.wikipedia.org/wiki/Research_on_meditation
Yoga:
https://nccih.nih.gov/health/yoga/introduction.htm#hed5
Acupuncture:
I just don't see how any of these can _possibly_ resolve _obstructive_ sleep apnea. For example, if you have a large tongue and it collapses in your sleep, I don't see how you can solve that by meditating. That's physically impossible.
It's very easy to see whether something has any sort of effect on your apnea; you sleep every night, and the difference is readily noticeable.
So the point is to perhaps be a bit more open minded and look into someone's suggestion rather than writing them off with a snide comment. There may or may not be something more to what they are saying, but you will never know if you think you somehow have the upper hand on truth over everyone else that ever existed.