On Busemann Surface Area of the Unit Ball in Minkowski Spaces

摘要

For a given -dimensional Minkowski space (finite dimensional Banach space) with unit ball , one can define the concept of surface area in different ways when . There exist two well-known definitions of surface area: the Busemann definition and Holmes-Thompson definition of surface area. The purpose of this paper is to establish lower bounds for the surface area of the unit ball in a -dimensional Minkowski space in case of Busemann's definition, when .