On the surface tension of fluctuating quasi-spherical vesicles.

We calculate the stress tensor for a quasi-spherical vesicle and we thermally average it in order to obtain the actual, mechanical, surface tension tau of the vesicle. Both closed and poked vesicles are considered. We recover our results for tau by differentiating the free energy with respect to the proper projected area. We show that tau may become negative well before the transition to oblate shapes and that it may reach quite large negative values in the case of small vesicles. This implies that spherical vesicles may have an inner pressure lower than the outer one.