Deforming convex bodies in Minkowski geometry

We introduce and study certain deformation of Minkowski norms in Rn (n ≥ 2) determined by a set of p < n linearly independent 1-forms and a smooth positive function of p variables. In particular, the deformation of a Euclidean norm α produces a Minkowski norm defined in our recent work; its indicatrix is a rotation hypersurface with a p-dimensional axis passing through the origin. For p = 1, our deformation generalizes the construction of (α,β)-norms which form a rich class of "computable"Minkowski norms and play an important role in Finsler geometry. We characterize such pairs of a Minkowski norm and its image that Cartan torsions of the two norms either coincide or differ by a C-reducible term. We conjecture that for n = 2 any Minkowski norm can be approximated by images of a Euclidean norm.