The logarithmic Minkowski problem

The logarithmic Minkowski problem

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Gaoyong Zhang , Polytechnic Institute of New York University
Rutgers - Hill Center, Room 705

The logarithmic Minkowski problem asks for necessary and sufficient conditions in order that a nonnegative finite Borel measure in (n-1)-dimensional projective space be the cone-volume measure of the unit ball of an n-dimensional Banach space. The solution to this problem is presented. Its relation to conjectured geometric inequalities that are stronger than the classical Brunn-Minkowski inequality will be explained.