Long-range elastic forces between membrane inclusions in spherical vesicles

We compute the elastic interaction between two identical conical inclusions in a spherical vesicle. We find it always repulsive and proportional to the square of the contact angle. At small angular separations Theta it decays as Theta(-4), as in the case of planar membranes. After a crossover Theta(c) similar to psi(0.54) where psi is the inclusions' aperture, it decays as Theta(-0.33), yielding a much stronger force than in a flat membrane. Finally, a quadratic minimum around the anti-polar configuration Theta = pi is reached.