Positivity of character subbundles and minimum principle for noncompact group actions

Abstract

Based on the results of Berndtsson on the positivity of holomorphic vector bundles associated to holomorphic fibration, we prove that, under the setting of the compact Lie group actions, the character subbundles of such bundles are holomorphic vector bundles and positive in the sense of Nakano. The second main purpose of the present paper is to establish Berndtsson’s integral form of Kiselman’s minimum principle in the setting of the noncompact Lie group actions.