Some logarithmic Minkowski inequalities for nonsymmetric convex bodies and related problems

Abstract

Abstract In this paper, we show the existence of a solution to an even logarithmic Minkowski problem for p-capacity and prove some analogue inequalities of the logarithmic Minkowski inequality for general nonsymmetric convex bodies involving p-capacity.

Keywords

• Logarithmic Minkowski inequality
• Logarithmic Minkowski problem
• p-capacity