Two main innovations are presented in this article. (1) The first reproducible synthesis of silicon carbide nanotubes of different internal and external diameters, The method used, the shape memory synthesis, is based on the gas-solid reaction between a vapor of SiO and nanotubes of carbon for the high diameters, and nanofibers of carbon for the small diameters. (2) A significant increase in the rate of a catalytic reaction (oxidation of H2S in S) probably due to a microscopic increase of the partial pressure of H2S inside the nanotubes, produced by condensation and microcapillarity, while the macroscopic partial pressure outside the tubes remains unchanged. This phenomenon could be extended to many other reactions, with polar gaseous reactants which are prone to condensation by capillarity at the usual temperatures of catalytic reaction, or with liquid phase reaction by an overconcentration of one of the reactants inside the tubes.