The Santal\'o point for the Holmes-Thompson boundary area

We explore the notion of Santal'o point for the Holmes-Thompson boundary area of a convex body in a normed space. In the case where the norm is $C^1$, and in the case where unit ball and convex body coincide, we prove existence and uniqueness. When the normed space has a smooth positively curved unit ball, we exhibit a dual Santal'o point expressed as an average of centroids of projections of the dual body.