# Existence of pseudo-heavy fibers of moment maps

## TL;DR

This paper introduces pseudo-heaviness in symplectic geometry, proves the existence of pseudo-heavy fibers of moment maps, and extends results on non-displaceable fibers, including applications to generalized coupled angular momenta.

## Contribution

It generalizes Entov and Polterovich's theorem by establishing the existence of pseudo-heavy fibers, providing a partial answer to their open problem.

## Key findings

- Existence of pseudo-heavy fibers in symplectic manifolds
- Generalization of non-displaceable fiber results
- Multiple non-displaceable fibers in specific systems

## Abstract

In the present paper, we introduce the notion of pseudo-heaviness of closed subsets of closed symplectic manifolds and prove the existence of pseudo-heavy fibers of moment maps. In particular, we generalize Entov and Polterovich's theorem, which ensures the existence of non-displaceable fibers, and provide a partial answer to a problem posed by them, which asks the existence of heavy fibers. Moreover, we apply our results to prove that some generalized coupled angular momenta have more than two non-displaceable fibers.