On Busemann Surface Area of the Unit Ball in Minkowski Spaces
نویسندگان
چکیده
For a given d-dimensional Minkowski space (finite dimensional Banach space) with unit ball B, one can define the concept of surface area in different ways when d ≥ 3. There exist two well-known definitions of surface area: the Busemann definition and HolmesThompson definition of surface area. The purpose of this paper is to establish lower bounds for the surface area of the unit ball in a d-dimensional Minkowski space in case of Busemann’s definition, when d ≥ 3.
منابع مشابه
On the Busemann Area in Minkowski Spaces
Among the different notions of area in a Minkowski space, those due to Busemann and to Holmes and Thompson, respectively, have found particular attention. In recent papers it was shown that the Holmes-Thompson area is integral-geometric, in the sense that certain integral-geometric formulas of Croftontype, well known for the area in Euclidean space, can be carried over to Minkowski spaces and t...
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