Unitarity and geometrical aspects at low x

On the grounds of extension of the U-matrix unitarization to the off-shell scattering we consider virtual-photon induced scattering. We discuss behavior of the structure function F_2(x,Q^2) at low x and the total cross-section of virtual-photon proton scattering and obtain, in particular, the dependence sigma^{tot}_{gamma^*p}\sim(W^2)^{lambda(Q^2)}, where exponent lambda(Q^2) is related to the interaction radius of a virtual constituent quark.