We give a systematic treatment of the stability theory for action of a real reductive Lie group G on a topological space. More precisely, we introduce an abstract setting for actions of noncompact real reductive Lie groups on topological spaces that admit functions similar to the KempfâNess function. The point of this construction is that one can characterize stability, semi-stability and polystability of a point by numerical criteria, that is in terms of a function called maximal weight. We apply this setting to the actions of a real noncompact reductive Lie group G on a real compact submanifold M of a KÃ¤hler manifold Z and to the action of G on measures of M.
|Appare nelle tipologie:||1.1 Articolo su rivista|