Related papers: Maximum principles in symplectic homology
We develop criteria for affine varieties to admit uniruled subvarieties of certain dimensions. The measurements are from long exact sequences of versions of symplectic cohomology, which is a Hamiltonian Floer theory for some open symplectic…
In this paper, we construct a Hamiltonian Floer theory based invariant called relative symplectic cohomology, which assigns a module over the Novikov ring to compact subsets of closed symplectic manifolds. We show the existence of…
We construct absolute and relative versions of Hamiltonian Floer homology algebras for strongly semi-positive compact symplectic manifolds with convex boundary, where the ring structures are given by the appropriate versions of the…
We introduce a combination of fixed point Floer homology and symplectic homology for Liouville domains. As an application, we detect non-trivial elements in the symplectic mapping class group of a Liouville domain.
We introduce a new package of Floer data of $\lambda$-sectorial almost complex structures $J$ and sectorial Hamiltonians $H$ on the Liouville sectors introduced by Ganatra-Pardon-Shende the pairs of which are amenable to the maximum…
We prove that when Hodge theory survives on non-compact symplectic manifolds, a compact symplectic Lie group action having fixed points is necessarily Hamiltonian, provided the associated almost complex structure preserves the space of…
We prove the existence of infinitely many periodic orbits of symplectomorphisms isotopic to the identity if they admit at least one hyperbolic periodic orbit and satisfy some condition on the flux. Our result is proved for a certain class…
We prove a contact non-squeezing phenomenon on homotopy spheres that are fillable by Liouville domains with infinite dimensional symplectic homology: there exists a smoothly embedded ball in such a sphere that cannot be made arbitrarily…
In this paper we first apply the chain level Floer theory to the study of Hofer's geometry of Hamiltonian diffeomorphism group in the cases without quantum contribution: we prove that any quasi-autonomous Hamiltonian path on weakly exact…
We use quantum and Floer homology to construct (partial) quasi-morphisms on the universal cover of the group of compactly supported Hamiltonian diffeomorphisms for a certain class of non-closed strongly semi-positive symplectic manifolds…
In this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of $b^m$-symplectic manifolds. Novel techniques are introduced to associate smooth symplectic forms to the…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…
Floer invented his theory in the mid eighties in order to prove the Arnol'd conjectures on the number of fixed point of Hamiltonian diffeomorphisms and Lagrangian intersections. Over the last thirty years, many versions of Floer homology…
We prove the existence of infinitely many periodic points of symplectomorphisms isotopic to the identity if they admit at least one (non-contractible) hyperbolic periodic orbit and satisfy some condition on its flux. The obtained periodic…
Given a closed, oriented surface, possibly with boundary, and a mapping class, we obtain sharp lower bounds on the number of fixed points of a surface symplectomorphism (i.e. area-preserving map) in the given mapping class, both with and…
This paper studies how symplectic invariants created from Hamiltonian Floer theory change under the perturbations of symplectic structures, not necessarily in the same cohomology class. These symplectic invariants include spectral…
The group of compactly supported Hamiltonian diffeomorphisms of a symplectic manifold is endowed with a natural bi-invariant distance, due to Viterbo, Schwarz, Oh, Frauenfelder and Schlenk, coming from spectral invariants in Hamiltonian…
Let (M,\omega) be a compact symplectic manifold, and \phi be a symplectic diffeomorphism on M, we define a Floer-type homology FH_*(\phi) which is a gen- eralization of Floer homology for symplectic fixed points defined by Dostoglou and…
In this paper, we develop a mini-max theory of the action functional over the semi-infinite cycles via the chain level Floer homology theory and construct spectral invariants of Hamiltonian diffeomorphisms on arbitrary, especially on {\it…
The necessity of a Maximum Principle arises naturally when one is interested in the study of qualitative properties of solutions to partial differential equations. In general, to ensure the validity of these kind of principles one has to…