Finsler geometrization of classic theory for fields on the interphase boundary including monomolecular 2D-system

We prove that the Ricci scalar curvature and the Berwald scalar curvature of a two-dimensional Finsler space, considered over a vector field on the 3-dimensional flat space, are naturally related to 2-dimensional electro-capillary phenomena effects observed for a compressed monolayer. The Cartan tensor and the nonlinear Barthel connection of the Finsler model are determined, and the geometric objects which depend on compression speed and on the characteristics of the electrically charged double layer are used in order to reveal several classes of structure formation within the phase transition of the first order.