  Field electron emission from nanometer-scale objects deviates from the
predictions of the classical emission theory as both the electrostatic
potential curves within the tunneling region and the image potential deviates
from the planar one. This impels the inclusion of additional correction terms
in the potential barrier. At the apex of a tip-like rotationally symmetric
surface, these terms are proportional to the (single) local emitter curvature.
The present paper generalizes this relation, showing that for any emitter
geometry, the coefficient of the correction terms is given by the mean
curvature, i.e. the average of the two principal curvatures.
