In continuous transportation models, minimum-cost paths are obtained by variational methods, in analogy with geometrical optics. Previous contributions on this subject have stated the appropriate Euler equations and discussed the possibility of defining a transportation-cost surface on which optimal paths are geodesics. The present paper discusses the sufficiency conditions for optimal paths and the existence conditions for cost surfaces, in terms of Gaussian theory. It is also demonstrated that, when the transportation model is isotropic, the cost surface is conformal to the plane.
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