Stability of the Borell–Brascamp–Lieb Inequality for Multiple Power Concave Functions

Abstract

In this paper, we prove the stability of the Brunn–Minkowski inequality for multiple convex bodies in terms of the concept of relative asymmetry. Using these stability results and the relationship of the compact support of functions, we establish the stability of the Borell–Brascamp–Lieb inequality for multiple power concave functions via relative asymmetry.

Keywords

• Borell–Brascamp–Lieb inequality
• Brunn–Minkowski inequality
• stability