  On elastic spherical membranes, there is no stress induced by the bending
energy and the corresponding Laplace-Young law does not involve the elastic
bending stiffness. However, when considering an axially symmetrical
perturbation that pinches the sphere, it induces nontrivial stresses on the
entire membrane. In this paper we introduce a theoretical framework to examine
the stress induced by perturbations of geometry around the sphere. We find the
local balance force equations along the normal direction to the vesicle, and
along the unit binormal, tangent to the membrane; likewise, the global balance
force equation on closed loops is also examined. We analyze the distribution of
stresses on the membrane as the budding transition occurs. For closed membranes
we obtain the modified Young-Laplace law that appears as a consequence of this
perturbation.
