Maximum principles in symplectic homology

Will J. Merry*, Igor Uljarevic

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 prove existence results for translated points.

Original languageEnglish
Pages (from-to)39-65
Number of pages27
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 1 Jan 2019
Externally publishedYes


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