  It is well known that relativistic hydrodynamics provides very good
description of heavy-ion collisions at RHIC/LHC energies up to transverse
momenta $p_\perp\sim 2\, \text{GeV}$. In this paper, we suggest that this
description can be extended to higher $p_\perp\sim 6\, \text{GeV}$, beyond
which hard collisions contribute. While most previous work focused on a part of
the freezeout surface at the latest proper time (referred to in this work as
the "lid"), we focus on the complementary part, to be referred as "the outer
edge," where the highest transverse rapidity of flow $\kappa\sim 1.4$ is
achieved. We study this surface analytically, using the Riemann rarefaction
wave, and numerically, using MUSIC numerical hydrodynamic code. We also use an
improved freezeout condition, where the collision rate equals the expansion
rate. For central collisions, we observe good description of spectra for
$\pi,K,N$ in central PbPb LHC collisions in this extended region. We further
suggest that "the outer edge" has very small azimuthal asymmetry even for
non-central collisions, smaller than predicted by standard hydrodynamics.
