In 2010, convex geometry began to be introduced into Orlicz space and gradually generated the Orlicz Brunn-Minkowski theory. In the past ten years, the theory has attracted the attention and research of many scientists.

Concepts such as mixed volumes, affine surface areas, quermassintegrals, affine quermassintegrals, projection bodies, and intersecting bodies have been extended to Orlicz space. The corresponding classical isoperimetric inequalities are also established in this space and yield the Orlicz Minkowski inequality and Orlicz Brunn-Minkowski inequality.

The aims of this Special Issue are to collate original research and review articles that further expand and develop the problem of convex geometry to Orlicz space. We welcome in-depth studies of existing problems and some problems that have never been solved. We encourage submissions relating to new concepts and inequalities of Orlicz space and the related problems in the dual theory. We hope also to attract review articles which describe the current state of the art.

Potential topics include but are not limited to the following:

• Orlicz affine, quermassintegral and Orlicz-Aleksandrov-Fenchel inequalities
• Orlicz dual affine quermassintegral and dual Orlicz-Aleksandrov-Fenchel inequalities
• Olicz affine surface area and related inequalities
• Orlicz Blaschke-Minkowski homomorphisms and related inequalities
• Orlicz logarithmic Aleksandrov-Fenchel inequalities