Morimichi Kawasaki, Ryuma Orita
Communications in Contemporary Mathematics 23 (05) 2050047 - 2050047 0219-1997 2020/07/07
[Refereed][Not invited] In this paper, we introduce the notion of pseudoheaviness of closed subsets of closed symplectic manifolds and prove the existence of pseudoheavy fibers of moment maps. In particular, we generalize Entov and Polterovich’s theorem, which ensures the existence of non-displaceable fibers. As its application, we provide a partial answer to a problem posed by them, which asks the existence of heavy fibers. Moreover, we obtain a family of singular Lagrangian submanifolds in [Formula: see text] with various rigidities.