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We discuss the question of how the number of dimensions of space and time caninfluence the equilibrium configurations of stars. We find that dimensionalitydoes increase the effect of mass but not the contribution of the pressure,which is the same in any dimension. In the presence of a (positive)cosmological constant the condition of hydrostatic equilibrium imposes a lowerlimit on mass and matter density. We show how this limit depends on the numberof dimensions and suggest that $\Lambda > 0$ is more effective in 4D than inhigher dimensions. We obtain a general limit for the degree of compactification(gravitational potential on the boundary) of perfect fluid stars in$D$-dimensions. We argue that the effects of gravity are stronger in 4D than inany other number of dimensions. The generality of the results is alsodiscussed

Hydrostatic Equilibrium of a Perfect Fluid Sphere with Exterior Higher-Dimensional Schwarzschild Spacetime