Cyclic Brunn-Minkowski Inequalities for <i>p</i>-affine surface area

Abstract

In 2010, Werner and Ye extended the denition for mixed p-affine surface area to all real numbers p. Following this, we establish some isoperimetric inequalities for the general mixed p-affine surface area. The results in special cases yield some of the recent results on inequalities of this type.

Mathematics Subject Classication (2010): 52A40, 46E30.

Key words: Affine surface area, mixed p-affine surface area, Brunn-Minkowski inequality,
general mixed p-affine surface area.