Dual Affine invariant points Mathieu MeyerCarsten SchuettElisabeth Werner 52A2053A15affine invariant pointdual affine invariant point An affine invariant point on the class of convex bodies $\mathcal{K}_n$ in $\mathbb{R}^n$, endowed with the Hausdorff metric, is a continuous map from $\mathcal{K}_n$ to $\mathbb{R}^n$ that is invariant under one-to-one affine transformations $A$ on $\mathbb{R}^n$, that is, $p(A(K))=A(p(K))$. We define here the new notion of dual affine point $q$ of an affine invariant point $p$ by the formula $q(K^{p(K)})=p(K)$ for every $K\in\mathcal{K}_n$, where $K^{p(K)}$ denotes the polar of $K$ with respect to $p(K)$. We investigate which affine invariant points do have a dual point, whether this dual point is unique and has itself a dual point. We also define a product on the set of affine invariant points, in relation with duality. Finally, examples are given which exhibit the rich structure of the set of affine invariant points. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5514 10.1512/iumj.2015.64.5514 en Indiana Univ. Math. J. 64 (2015) 735 - 768 state-of-the-art mathematics http://iumj.org/access/