Corrections to the Laplace law for vesicle aspiration in micropipettes and other confined geometries

Based on the stress tensor associated with the Helfrich Hamiltonian, we study how the Laplace law is modified for fluid lipid membranes under small tensions or constrained within small scale devices. We derive several exact analytical results corresponding to global or local generalized Laplace relations. Analytical and numerical results based on standard energy minimization confirm these exact relations and further quantify the deviations of the standard Laplace law.