We employ a mean-field theory to study ground-state properties and transport

of a two-dimensional gas of ultracold alklaline-earth metal atoms governed by

the Kondo Lattice Hamiltonian plus a parabolic confining potential. In a

homogenous system this mean-field theory is believed to give a qualitatively

correct description of heavy fermion metals and Kondo insulators: it reproduces

the Kondo-like scaling of the quasiparticle mass in the former, and the same

scaling of the excitation gap in the latter. In order to understand

ground-state properties in a trap we extend this mean-field theory via

local-density approximation. We find that the Kondo insulator gap manifests as

a shell structure in the trapped density profile. In addition, a strong

signature of the large Fermi surface expected for heavy fermion systems

survives the confinement, and could be probed in time-of-flight experiments.

From a full self-consistent diagonalization of the mean-field theory we are

able to study dynamics in the trap. We find that the mass enhancement of

quasiparticle excitations in the heavy Fermi liquid phase manifests as slowing

of the dipole oscillations that result from a sudden displacement of the trap

center.