  We present observations of the molecular gas in the nuclear environment of
three prototypical low luminosity AGN (LLAGN), based on VLT/SINFONI AO-assisted
integral-field spectroscopy of H2 1-0 S(1) emission at angular resolutions of
~0.17". On scales of 50-150 pc the spatial distribution and kinematics of the
molecular gas are consistent with a rotating thin disk, where the ratio of
rotation (V) to dispersion (sigma) exceeds unity. However, in the central 50
pc, the observations reveal a geometrically and optically thick structure of
molecular gas (V/sigma<1 and N_H>10^{23} cm^{-2}) that is likely to be
associated with the outer extent of any smaller scale obscuring structure. In
contrast to Seyfert galaxies, the molecular gas in LLAGN has a V/sigma<1 over
an area that is ~9 times smaller and column densities that are in average ~3
times smaller. We interpret these results as evidence for a gradual
disappearance of the nuclear obscuring structure. While a disk wind may not be
able to maintain a thick rotating structure at these luminosities, inflow of
material into the nuclear region could provide sufficient energy to sustain it.
In this context, LLAGN may represent the final phase of accretion in current
theories of torus evolution. While the inflow rate is considerable during the
Seyfert phase, it is slowly decreasing, and the collisional disk is gradually
transitioning to become geometrically thin. Furthermore, the nuclear region of
these LLAGN is dominated by intermediate-age/old stellar populations (with
little or no on-going star formation), consistent with a late stage of
evolution.
