  A communication network is a graph in which each node has only local
information about the graph and nodes communicate by passing messages along its
edges. Here, we consider the {\it geometric communication network} where the
nodes also occupy points in space and the distance between points is the
Euclidean distance. Our goal is to understand the communication cost needed to
solve several fundamental geometry problems, including Convex Hull, Diameter,
Closest Pair, and approximations of these problems, in the asynchronous CONGEST
KT1 model. This extends the 2011 result of Rajsbaum and Urrutia for finding a
convex hull of a planar geometric communication network to networks of
arbitrary topology.
