Variants of Hörmander’s theorem on q-convex manifolds by a technique of infinitely many weights

Abstract

By introducing a new approximation technique in the \(L^2\) theory of the \(\bar{\partial }\)-operator, Hörmander’s \(L^2\) variant of Andreotti-Grauert’s finiteness theorem is extended and refined on q-convex manifolds and weakly 1-complete manifolds. As an application, a question on the \(L^2\) cohomology suggested by a theory of Ueda (Tohoku Math J (2) 31(1):81–90, 1979), Ueda (J Math Kyoto Univ 22(4):583–607, 1982/83) is solved.