  We define and investigate the consensus problem for a set of $N$ processes
embedded on the $d$-dimensional plane, $d\geq 2$, which we call the {\em
geoconsensus} problem. The processes have unique coordinates and can
communicate with each other through oral messages. In contrast to the
literature where processes are individually considered Byzantine, it is
considered that all processes covered by a finite-size convex fault area $F$
are Byzantine and there may be one or more processes in a fault area. Similarly
as in the literature where correct processes do not know which processes are
Byzantine, it is assumed that the fault area location is not known to the
correct processes. We prove that the geoconsensus is impossible if all
processes may be covered by at most three areas where one is a fault area.
  Considering the 2-dimensional embedding, on the constructive side, for $M
\geq 1$ fault areas $F$ of arbitrary shape with diameter $D$, we present a
consensus algorithm that tolerates $f\leq N-(2M+1)$ Byzantine processes
provided that there are $9M+3$ processes with pairwise distance between them
greater than $D$. For square $F$ with side $\ell$, we provide a consensus
algorithm that lifts this pairwise distance requirement and tolerates $f\leq
N-15M$ Byzantine processes given that all processes are covered by at least
$22M$ axis aligned squares of the same size as $F$. For a circular $F$ of
diameter $\ell$, this algorithm tolerates $f\leq N-57M$ Byzantine processes if
all processes are covered by at least $85M$ circles. We then extend these
results to various size combinations of fault and non-fault areas as well as
$d$-dimensional process embeddings, $d\geq 3$.
