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A continuous transformation from a closed vesicle to an open vesicle needsthat the area of open hole enlarge from zero. Since the shape equation andboundary conditions of lipid open vesicles with free edges have been obtained,we want know whether this process can be archived with valid parameters. Bystudy the boundary conditions in the axisymmetric case, the analytic expressionof the boundary edges is obtained generally. It reveals that the radius andline tension of boundary edges are confined strongly by bending moduli. In somecases, there is the minimal nonzero boundary radius and the line tension needsto surmount the maxim following the increase of boundary radius. Without thespontaneous curvature, the line tension will trend to infinite when theboundary radius shrinks to zero. The continuous opening process from a closedvesicle to an open vesicle needs that the spontaneous curvature is nonzero andthe ratio between the bending moduli of Gauss curvature and mean curvaturesatisfies $k\leq-4$. Besides the line tension, a closed vesicle can be openedthrough changing the spontaneous curvature.

Boundary behaviours of open vesicles in axisymmetric case