Extensions of a Bonnesen-style inequality to Minkowski spaces

Abstract

Various definitions of surface area and volume are possible in finite dimensional normed linear spaces (= Minkowski spaces). Using a Bonnesen-style inequality, we investigate the ratio of the Holmes-Thompson surface area of the unit ball to its volume. In particular, in the planar case a stronger lower bound for this ratio is established when the area is defined in the sense of Holmes-Thompson, or is given by the definition of mass. From this we obtain some (characteristic) properties of Radon curves. Mathematics subject classification (2000): 52A10, 52A21, 52A40, 46B20.