Bounds on some geometric functionals of high dimensional Brownian convex hulls and their inverse processes

We prove two-sided bounds on the expected values of several geometric functionals of the convex hull of Brownian motion in Rⁿ and their inverse processes. This extends some recent results of McRedmond and Xu (2017), Jovaleki\'{c} (2021), and Cygan, \Sebek, and the first author (2023) from the plane to higher dimensions. All of our bounds capture the correct order of asymptotic growth or decay in the dimension n.