Geometric Bounds on Kaluza-Klein Masses
  We point out geometric upper and lower bounds on the masses of bosonic and fermionic Kaluza-Klein excitations in the context of theories with large extra dimensions. The characteristic compactification length scale is set by the diameter of the internal manifold. Based on geometrical and topological considerations, we find that certain choices of compactification manifolds are more favoured for phenomenological purposes. 
Avijit Mukherjee and Rula Tabbash