A characterization of the support map

作者：Artstein Avidan S^*; Milman V

来源：Advances in Mathematics, 2010, 223(1): 379-391.

DOI：10.1016/j.aim.2009.07.020

• Characterization
• Support

In this short note we give a characterization of the support map from classical convexity. We show it is the unique additive transformation from the class of closed convex sets in R(n) which include 0 to the class of positive 1-homogeneous functions on R(n). This will be a consequence of a theorem about transforms from the class of convex sets to itself which preserve Minkowski addition.

• 出版日期2010-1-15