  Lipid membrane with freely exposed edge is regarded as smooth surface with
curved boundary. Exterior differential forms are introduced to describe the
surface and the boundary curve. The total free energy is defined as the sum of
Helfrich's free energy and the surface and line tension energy. The equilibrium
equation and boundary conditions of the membrane are derived by taking the
variation of the total free energy. These equations can also be applied to the
membrane with several freely exposed edges. Analytical and numerical solutions
to these equations are obtained under the axisymmetric condition. The numerical
results can be used to explain recent experimental results obtained by Saitoh
\emph{et al}. [Proc. Natl. Acad. Sci. \textbf{95}, 1026 (1998)].
