On the generalization of the average chord length

Recently, it has been proved that the well-known mean chord length property remains valid for some diffusive processes in bounded domains. Based on the one-velocity linear Boltzmann transport equation, this result can be extended to spaces of constant curvature. Besides, for straight lines, inequalities for the ray distribution (starting point inside the domain and exiting point on the surface of the object) are derived using simple tools from integral geometry in .