  New Orlicz Brunn-Minkowski inequalities are established for rigid motion
compatible Minkowski valuations of arbitrary degree. These extend classical
log-concavity properties of intrinsic volumes and generalize seminal results of
Lutwak and others. Two different approaches which refine previously employed
techniques are explored. It is shown that both lead to the same class of
Minkowski valuations for which these inequalities hold. An appendix by Semyon
Alesker contains the proof of a new classification of generalized translation
invariant valuations.
