  We perform a detailed analysis of quarter BPS bubbling geometries with AdS
asymptotics and their corresponding duality relations with their dual states in
the quantum field theory side, among other aspects. We derive generalized
Laplace-type equations with sources, obtained from linearized Monge-Ampere
equations, and used for asymptotically AdS geometry. This enables us to obtain
solutions specific to the asymptotically AdS context. We conduct a thorough
analysis of boundary conditions and explore the stretched technique where
boundary conditions are imposed on a stretched surface. These boundary
conditions include grey droplets. This stretched technique is naturally used
for the superstar, where we place grey droplet boundary conditions on the
stretched surface. We also perform a coarse-graining of configurations and
analyze the symplectic forms on the configuration space and their
coarse-graining.
