The Logarithmic Minkowski Problem
K\'aroly J. B\"or\"oczky, Erwin Lutwak, Deane Yang, Gaoyong Zhang
TL;DR
This paper addresses the logarithmic Minkowski problem by establishing necessary and sufficient conditions for a measure on the sphere to be the cone-volume measure of a Banach space's unit ball, advancing geometric analysis.
Contribution
It provides a complete characterization of measures corresponding to cone-volume measures in the context of the logarithmic Minkowski problem.
Findings
Characterization of cone-volume measures for Banach space unit balls.
Necessary and sufficient conditions for measures on the sphere.
Advancement in understanding the geometric structure of Banach spaces.
Abstract
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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