  This article contains both a point process and a sequential description of
the greatest convex minorant of Brownian motion on a finite interval. We use
these descriptions to provide new analysis of various features of the convex
minorant such as the set of times where the Brownian motion meets its minorant.
The equivalence of the these descriptions is non-trivial, which leads to many
interesting identities between quantities derived from our analysis. The
sequential description can be viewed as a Markov chain for which we derive some
fundamental properties.

Probability