TY - JOUR
T1 - Maximum principles in symplectic homology
AU - Merry, Will J.
AU - Uljarevic, Igor
N1 - Publisher Copyright:
© 2018, Hebrew University of Jerusalem.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85055754164&partnerID=8YFLogxK
U2 - 10.1007/s11856-018-1792-z
DO - 10.1007/s11856-018-1792-z
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AN - SCOPUS:85055754164
SN - 0021-2172
VL - 229
SP - 39
EP - 65
JO - Israel Journal of Mathematics
JF - Israel Journal of Mathematics
IS - 1
ER -