If I understand correctly, Gauss proved that given any oriented Riemannian surface, one can find a complex structure on the surface so that the metric on the charts is just $f|dz|$, where $f>0$.
I've heard these coordinates referred as "conformal coordinates," which makes sense, but I've also heard of them referred to as "isothermal coordinates."
Why are these coordinates called "isothermal"? Who named it "isothermal"? Does it have anything to do with physics, or is it kind of like "Inertia"?