In this talk, I will discuss the stability of two inequalities: “Alexandrov-Fenchel inequalities in hyperbolic space” and “Minkowski’s inequality in a general warped product space.” I will give a brief overview of both inequalities and their respective stability problems. To understand what I mean by stability, I will first discuss it for Isoperimetric inequality, which is a special case of Alexandrov-Fenchel inequalities. I will also briefly discuss the idea of proofs in both these cases and some of my own results in this field. This is joint work with Prof. Dr. Julian Scheuer.