  The minimum energy path (MEP) is the most probable transition path that
connects two equilibrium states of a potential energy landscape. It has been
widely used to study transition mechanisms as well as transition rates in the
fields of chemistry, physics, and materials science. In this paper, we derive a
novel result establishing the stability of MEPs under perturbations of the
energy landscape. The result also represents a crucial step towards studying
the convergence of various numerical approximations of MEPs, such as the nudged
elastic band and string methods.
