where do you apply the liquid wrench? on the top of the bike by the headset? Or do you put the bike upside down and pour the liquid wrench into the hole at the bottom of the fork?

Thread is old - but the situation is frequent, so here is the success story of removing a frozen Pivo stem from a Motobecane frame.
Three methods were tried:
1. Thread the top of the stem (where the bolt goes), screw in a bolt, turn the bike over, and use a slide hammer to pull out a stem. Failed, but we had a relatively small hammer - with a larger hammer it would have worked.
3. Next thing, we pounded the stem *down*, into the tube, to break the bond. That worked - we gained couple of millimeters. Then..
2. Turn the bike over, place the top tube on a good support, closer to the headtube joint (resilient, but pliant- we used a large thick fiberboard panel, but vertically placed 2x4 or 2x6 will probably to just fine.). Cut a piece of wood on a angle (we used thick plywood; solid wood is likely to split), so it fits nicely into the bend of the typical quill stem from underneath (of course, now the bike is upside down, so the angled stem underbelly is facing up).
This is obviously a better arranged variation on what we all tried to do - just use a mallet to pound the stem out. This doesn't work since you are hitting down->up, bike jumps up, etc., and besides, you are hitting handlebar clamp, which is not good enough. Turn bike over, support it from underneath, and use a wooden piece to transmit the blow to the right spot, just where the stem body joins the extension...

Just to throw in some of my experience.

I had a solid quill stem in my steerer, it was well seized inside due to the galvanic corrosion. Here's what I tried and failed at to full force, no holds barred.

1. Knocked the bolt down with a heavy hammer to dislodge the wedge - wedge dropped, no stem movement.
2. Clamped forks in a bench vice and twisted/pulled up on bars - didn't budge.
3. Pour neat ammonium hydroxide (you can just call it concentrated ammonia - the strongest aqueous ammonia you can get) with bike upside down and tried down the top and left to soak several times overnight. Tried again in the bench vice. Still solid.
4. Tried breaking the bond by hammering on the top of the stem with the bottom of the steerer tub on a solid metal bar to the ground. Tried to push the stem further in the steerer tube just to break the bond. Stem didn't budge a micron.
5. Tried a large screw press on the top of the stem and under the steerer tube to squash the stem into the steerer tube and break the bond. Again to no avail.

At this point there was only one thing left to try to keep my stem intact. That is liquid nitrogen or dry ice and acetone (or other low freezing liquid) to make a very cold liquid and pour down the steerer to cool the aluminium and cause it to shrink inside the tube. Unfortunately no access to dry ice or liquid nitrogen. I think this could work. The other alternative is a compressed CO2 canister turned upside down and sprayed inside.

So, final resort I had to damage my stem but I was was able to recover my forks after at least, I hacksawed off the top of the stem to remove the forks. I then (luckily for me and my place of work) put the forks in a bath of hot caustic soda (about 10-20 percent strength). This dissolved the aluminium left behind completely after several hours and I recovered my forks with a vacant steerer. If you have delicate paintwork this option wouldn't be viable. Fortunately for me I had stripped the paint on my bike so this removed the final traces of paint from the forks.

Don't try caustic to dissolve the alumium oxide if you want to retain the stem. It will just eat away at the stem and you will end up with one ugly looking and potentially fracture prone stem.

Hope this is useful and good luck.