  We derive the plasticity equations for convex quadrilaterals on a complete
convex surface with bounded specific curvature and prove a plasticity principle
which states that: Given four shortest arcs which meet at the weighted
Fermat-Torricelli point their endpoints form a convex quadrilateral and the
weighted Fermat-Torricelli point belongs to the interior of this convex
quadrilateral, an increase of the weight corresponding to a shortest arc causes
a decrease of the two weights that correspond to the two neighboring shortest
arcs and an increase of the weight corresponding to the opposite shortest arc
by solving the inverse weighted Fermat-Torricelli problem for quadrilaterals on
a convex surface of bounded specific curvature. Furthermore, we show a
connection between the plasticity of convex quadrilaterals on a complete convex
surface with bounded specific curvature with the plasticity of some generalized
convex quadrilaterals on a manifold which is certainly composed by triangles.
We also study some cases of symmetrization of weighted convex quadrilaterals by
introducing a new symmetrization technique which transforms some classes of
weighted geodesic convex quadrilaterals on a convex surface to parallelograms
in the tangent plane at the weighted Fermat-Torricelli point of the
corresponding quadrilateral.
