  In the recent literature it has been questioned whether the local
backreaction of antibranes in flux throats can induce a perturbative brane-flux
decay. Most evidence for this can be gathered for D6 branes and Dp branes
smeared over 6-p compact directions, in line with the absence of finite
temperature solutions for these cases. The solutions in the literature have
flat worldvolume geometries and non-compact transversal spaces. In this paper
we consider what happens when the worldvolume is AdS and the transversal space
is compact. We show that in these circumstances brane polarisation smoothens
out the flux singularity, which is an indication that brane-flux decay is
prevented. This is consistent with the fact that the cosmological constant
would be less negative after brane-flux decay. Our results extend recent
results on AdS_7 solutions from D6 branes to AdS_(p+1) solutions from Dp
branes. We show that supersymmetry of the AdS solutions depend on p
non-trivially.
