  We consider the Gierer-Meinhardt system with small inhibitor diffusivity and
very small activator diffusivity in a bounded and smooth two-dimensional
domain. For any given positive integer $k$ we construct a spike cluster
consisting of $k$ boundary spikes which all approach the same nondegenerate
local maximum point of the boundary curvature. We show that this spike cluster
is linearly stable.
  The main idea underpinning these stable spike clusters is the following: due
to the small inhibitor diffusivity the interaction between spikes is repulsive
and the spikes are attracted towards a nondegenerate local maximum point of the
boundary curvature. Combining these two effects can lead to an equilibrium of
spike positions within the cluster such that the cluster is linearly stable.
