||Monotone quantities along hypersurfaces evolving under the inverse mean curvature flow have many applications in geometry and relativity. In this talk, I will discuss a family of new monotone increasing quantities along inverse curvature flows in the Euclidean space. I will also discuss a
related Minkowski type formula and a geometric inequality for closed k-convex hypersurfaces. Part of it is joint work with Pengzi Miao.