Surface tension (S) is due to the inward force experienced by particles at the surface and usually gravitation does not play an important role in this force. But in compact stars the gravitational force on the particles is very large and S is found to depend not only on the interactions in the strange quark matter, but also on the structure of the star, i.e. on its mass and radius. Indeed, it has been claimed recently that 511 keV photons observed by the space probe INTEGRAL from the galactic bulge may be due to e+ e- annihilation, and their source may be the positron cloud outside of an antiquark star. Such stars, if they exist, may also go a long way towards explaining away the antibaryon deficit of the universe. For that to happen S must be high enough to allow for survival of quark/antiquark stars born in early stages of the formation of the universe. High value of S may also assist explanation of delayed γ-ray burst after a supernova explosion, as conversion from normal matter to strange matter takes place. The possibility of some implications from formation of surface waves are also discussed. © ESO 2005.