| Abstract: | In this paper, we study the Minkowski valuations on the set of 1 or 2 dimensional convex bodies compatible with a linear transformation and translations in some sense. We first introduce a kind of compatibility that all linear transformations(as Minkowski valuations) possess naturally. Then, we show that, under some natural conditions, monotone Minkowski valuations with such compatibility are exactly linear transformations. So we obtain a valuation characterization of linear transformations on Euclidean 1 or 2-spaces. |
