Use a hotplate at least as big as your pan in order to prevent warping
I read this in other question's answer. I have never heard of this before today. I had always believed that, as the core is aluminum, heat would be transferred from inside to outside if coil element was too small. Any links to vendor websites that state as such? I've looked, can't find anything specific.
Gas ranges don't even have a "size", so how is this handled?
So, first, burner size is only one reason why pans warp, and probably not the most common one.
Pans warp on burners due to uneven heating and cooling. One way that heating can be uneven is if the burner is much smaller than the pan; this means that it will heat up in the center but not as much around the edges. Since heated metal expands, this causes "bowing". Over time, the pan may stop flattening again once it's cool. Note that bowing can occur even over a large burner with a thin-bottomed pan.
This is a problem on all types of burners, but it's worst on induction burners. Gas flames tend to spread out regardless of how small the burner is, so they don't really concentrate in one spot. Electric resistance burners generate radiant heat as well as conductive, and as such offer some heating even to parts of the pan they don't touch. Inductive burners, however, heat only the parts of the pan they're in contact with, and do so very rapidly. When you combine that with the fact that induction burners tend to be smaller than gas or electric ones, you end up with a steep temperature differential between the part of the pan over the burner and the part that's not.
Chef Helen Rennie (video) documents this pretty well (with the caveat that she's a big fan of gas stoves).
As you guessed, several things about your pan increase or decrease the chances of warping, including pan thickness, material and conductivity, shape, and how well the pan makes contact with electric or induction burners.
Pan manufacturers do not provide guidance on this, probably because it would encourage people to buy smaller and cheaper pans.
Since I wrote the original answer, I'll chime in here too.
My statement was not based on some kind of written evidence, but on a combination of kitchen lore and personal experience. I have not only heard about it, but have seen warped pans in use and warped my pans myself. And as far as I can tell, there was burner size mismatch. Currently, the only warped pan in my own kitchen is larger than any plate I have, and it is warped middle up. I cannot exclude confirmation bias, but for now, I am quite confident that the effect is real.
As for the mechanism behind it: pans are not perfect conductors (in fact, some are rather poor conductors, and that's on purpose). If you heat only the middle of a pan's bottom, the middle will always be hotter than the outer parts, even though the parts will get hot too, just less so. So during the cooking, the pan can bulge up in the middle. I'm not a metallurgy expert, so I don't know why it doesn't contract back to its original state when it cools, but the observation is that some pans don't do it, and stay warped.
The gas burner is not like a hotplate, in that there is no strict border where heating stops. Instead, the flame warms up the air around it, and some hot air gets trapped under the pan bottom's middle, while some more air streams outwards. You can regulate the size of the hot area - the nozzles are pointed sideways, so more flame makes the burning ring larger - and burners intended for large pans are sometimes made with two rings.
If you are looking for more reliable confirmation, the manufacturers' and vendors' sites are the last place to go. Pan manufacturers are known for upholding the myth of infallible pans, just look at all the claims about coated pans, and compare them to reality. Better information might be had from third parties specializing in metal working, but I don't know where I'd search for this easily.
