# Maximum principles in symplectic homology

## TL;DR

This paper extends maximum principle techniques in symplectic homology to broader Hamiltonian classes, enabling new applications such as detecting infinite order elements in symplectic mapping class groups and proving translated point existence.

## Contribution

It introduces a generalized maximum principle for Floer solutions, broadening the class of Hamiltonians usable in symplectic homology constructions.

## Key findings

- Extended class of Hamiltonians for symplectic homology
- Detected elements of infinite order in symplectic mapping class groups
- Proved existence of translated points

## Abstract

In the setting of symplectic manifolds which are convex at infinity, we use a version of the Aleksandrov maximum principle to derive uniform estimates for Floer solutions that are valid for a wider class of Hamiltonians and almost complex structures than is usually considered. This allows us to extend the class of Hamiltonians which one can use in the direct limit when constructing symplectic homology. As an application, we detect elements of infinite order in the symplectic mapping class group of a Liouville domain, and obtain existence results for translated points.