Károly J. Böröczky, Erwin Lutwak, Deane Yang, Gaoyong Zhang
Abstract
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In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite-dimensional Banach space.
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In analogy with the classical Minkowski problem, necessary and sufficient conditions are given to assure that a given measure on the unit sphere is the cone-volume measure of the unit ball of a finite-dimensional Banach space.
Key concepts: Mathematics, Unit sphere, Minkowski space, Measure (data warehouse), Banach space, Logarithm, Cone (formal languages), Unit (ring theory)