For arbitrary convex bodies K,L in R^n, the mixed area measure S_{K,...,K,L} is supported exactly on the closure of the (K,...,K,L)-extreme directions, which resolves Schneider's conjecture in R^3 and gives the upper bound in all dimensions.
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On Minkowski's monotonicity problem
For arbitrary convex bodies K,L in R^n, the mixed area measure S_{K,...,K,L} is supported exactly on the closure of the (K,...,K,L)-extreme directions, which resolves Schneider's conjecture in R^3 and gives the upper bound in all dimensions.