L^2-Cohomology and complete Hamiltonian manifolds

Abstract

A classical theorem of Frankel for compact Kähler manifolds states that a Kähler S^1-action is Hamiltonian if and only if it has fixed points. We prove a metatheorem which says that when Hodge theory holds on non-compact manifolds, then Frankel's theorem still holds. Finally, we present several concrete situations in which the assumptions of the metatheorem hold.

14 pages. This article expands and improves on arxiv:1005.2163