Geometric conservation laws for perfect Y-branched carbon nanotubes

Based on the integral theorems for mean curvature and Gauss curvature, geometric conservation laws for perfect Y-branched carbon nanotubes are presented. From the conservation laws, simple geometric regulations observed by spontaneous Y-branched carbon nanotubes are revealed, i.e. the angle between two neighbouring branches should be 120 degrees. and the radii of the three branches should be equal. These results coincide well with all experimental facts without exceptions. Possible applications of the geometric regulations to the design of super carbon nanostructures with self-similarities are predicted.