A L2 estimate for the minimal solution of (partial derivative)over-bar on the unit ball

Summary: By considering intrinsic geometric conditions, a new class of domains in complex Euclidean space has been introduced, which is invariant under biholomorphism and includes several types of domains. It has been shown that for this class of domains, compactness of the a-Neumann operator on certain forms is equivalent to the boundary not containing any q-dimensional analytic varieties. Additionally, it has been proven that the Bergman metric is equivalent to the Kobayashi metric for this class of domains.