Dual Orlicz-Brunn-Minkowski theory: dual Orlicz Lφ affine and geominimal surface areas
Abstract
This paper aims to develop basic theory for the dual Orlicz Lφ affine and geominimal surface areas for star bodies, which belong to the recent dual Orlicz-Brunn-Minkowski theory for star bodies. Basic properties for these new affine invariants will be provided. Moreover, related Orlicz affine isoperimetric inequality, cyclic inequality, Santal\'o style inequality and Alexander-Fenchel type inequality are established.
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