ABSTRACT
In this chapter we consider physical problems related to two-dimensional flexible surfaces called membranes. A membrane may be defined as a thin film that bends but, in the present development, does not stretch. The boundary of the membrane may be fixed or free or have forces applied to it. We will also consider cases where the membrane interacts with the material in which it is embedded and is thus subject to external forces such as driving forces or friction. Examples of membranes include drum heads, flags, trampolines, soap films, and biological barriers such as cellular membranes. Surfaces of liquids may be treated as membranes under the appropriate circumstances.
