Abstract
These notes grew out of an expose on M. Gromov's paper "Convex sets and Kähler manifolds'' ("Advances in Differential Geometry and Topology,'' World Scientific, 1990) at the DMV-Seminar on "Combinatorical Convex Geometry and Toric Varieties'' in Blaubeuren in April `93. Gromov's paper deals with a proof of Alexandrov--Fenchel type inequalities and the Brunn--Minkowski inequality for finite dimensional compact convex sets and their variants for compact Kähler manifolds. The emphasis of these notes lies on basic details and the techniques from various mathematical areas involved in Gromov's arguments.
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