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Orlicz multiple affine quermassintegrals
Chang-Jian Zhao
Keywords:Lp-addition, Orlicz addition, affine quermassintegrals, Orlicz affine quermassintegrals, Orlicz multiple mixed volumes, Orlicz-Aleksandrov-Fenchel inequality.
      In the paper, our main aim is to generalize the mixed affine quer massintegrals to Orlicz space. We introduce a new affine geometric quan tity, and call it Orlicz multiple affine quermassintegrals. The mixed affine quermassintegrals and Aleksandrov-Fenchel type inequality are extended to an Orlicz setting, and the related concepts and inequalities of Orlicz mul tiple mixed volumes are also included in our conclusions. The new Orlicz Aleksandrov-Fenchel inequality in special cases yields Lp-Aleksandrov-Fenchel inequality and Orlicz-Aleksandrov-Fenchel inequality. As application, a new Orlicz-Brunn-Minkowski inequality for mixed affine quermassintegrals is estab lished.