Bundle-Convexity and Kernel Asymptotics on a Class of Locally Pseudoconvex Domains

A generalization of Grauert’s solution of the Levi problem for strongly pseudoconvex domains will be given. On a class of bounded locally pseudoconvex domains in complex manifolds, spaces of holomorphic sections of vector bundles are analyzed by the \(L^2\) method. Under appropriate positivity conditions on the curvature, a bundle-convexity theorem holds as a generalization of Grauert’s theorem. Based on it, function-theoretic properties of such domains will be discussed.