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On the basis of the integral theorems about the mean curvature and Gauss curvature, geometric conservation laws for cells or vesicles are proved. These conservation laws may depict various special bionano structures discovered in experiments, such as the membrane nanotubes and singular points grown from the surfaces of cells or vesicles. Potential applications of the conservation laws to lipid nanotube junctions that interconnect cells or vesicles are discussed.

Geometric conservation laws for cells or vesicles with membrane nanotubes or singular points.