  In the framework of the lubrication approximation, we derive a set of
equations describing the steady bottom profile of Leidenfrost drops coupled
with the vapor pressure. This allows to derive scaling laws for the geometry of
the concave bubble encapsulated between the drop and the hot plate under it.
The results agree with experimental observations in the case of droplets with
radii smaller than the capillary length Rc as well as in the case of puddles
with radii larger than Rc.
