51 citations · 209 across the 27 of their papers we have counts for
29 papers
The symplectic Hadamard question
Dan Cristofaro-Gardiner
We show that a simply connected symplectic manifold admitting a complete nonpositively curved compatible metric is symplectomorphic to R^{2n} with its standard symplectic form. Thi…
Topological symplectic manifolds and bi-Lipschitz structures
Dan Cristofaro-Gardiner, Boyu Zhang
We show that a topological symplectic manifold has a canonically associated bi-Lipschitz structure. As a corollary, we obtain the first examples of non-existence and non-uniqueness…
Symplectic Weyl Laws
Dan Cristofaro-Gardiner
We survey a number of Weyl type laws that have recently been established in low-dimensional symplectic geometry. These have had a number of applications, which we also introduce. W…
Low-dimensional topology and symplectic dynamics
Dan Cristofaro-Gardiner
These are notes to accompany my lectures at the "Current Developments in Mathematics" conference hosted by Harvard/MIT. The lectures were about some recent progress in our u…
Curvy points, the perimeter, and the complexity of convex toric domains
Dan Cristofaro-Gardiner, Nicki Magill, Dusa McDuff
We study the related notions of curvature and perimeter for toric boundaries and their implications for symplectic packing problems in dimension 4; a natural setting for this is a…
Low-action holomorphic curves and invariant sets
Dan Cristofaro-Gardiner, Rohil Prasad
We prove a compactness theorem for sequences of low-action punctured holomorphic curves of controlled topology, in any dimension, without imposing the typical assumption of uniform…
On the large-scale geometry of domains in an exact symplectic 4-manifold
Dan Cristofaro-Gardiner, Richard Hind
We show that the space of open subsets of any complete and exact symplectic -manifold has infinite dimension with respect to the symplectic Banach-Mazur distance; the quasi-flat…
Proof of Hofer-Wysocki-Zehnder's two or infinity conjecture
Dan Cristofaro-Gardiner, Umberto Hryniewicz, Michael Hutchings +1
We prove that every Reeb flow on a closed connected three-manifold has either two or infinitely many simple periodic orbits, assuming that the associated contact structure has tors…
On the agreement of symplectic capacities in high dimension
Dan Cristofaro-Gardiner, Richard Hind
A theorem of Gutt-Hutchings-Ramos asserts that all normalized symplectic capacities give the same value for monotone four-dimensional toric domains. We generalize this theorem to a…
Boundaries of open symplectic manifolds and the failure of packing stability
Dan Cristofaro-Gardiner, Richard Hind
A finite volume symplectic manifold is said to have "packing stability" if the only obstruction to symplectically embedding sufficiently small balls is the volume obstruction. Pack…
Subleading asymptotics of link spectral invariants and homeomorphism groups of surfaces
Dan Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak +2
This paper continues the study of link spectral invariants on compact surfaces, introduced in our previous work and shown to satisfy a Weyl law in which they asymptotically recover…
A note on the existence of U-cyclic elements in periodic Floer homology
Dan Cristofaro-Gardiner, Daniel Pomerleano, Rohil Prasad +1
Edtmair-Hutchings have recently defined, using periodic Floer homology, a U-cycle property for Hamiltonian isotopy classes of area-preserving diffeomorphisms of closed surfaces. Th…
Periodic Floer homology and the smooth closing lemma for area-preserving surface diffeomorphisms
Dan Cristofaro-Gardiner, Rohil Prasad, Boyu Zhang
We prove a very general Weyl-type law for Periodic Floer Homology, estimating the action of twisted Periodic Floer Homology classes over essentially any coefficient ring in terms o…
Quantitative Heegaard Floer cohomology and the Calabi invariant
Daniel Cristofaro-Gardiner, Vincent Humilière, Cheuk Yu Mak +2
We define a new family of spectral invariants associated to certain Lagrangian links in compact and connected surfaces of any genus. We show that our invariants recover the Calabi…
Higher Symplectic Capacities and the Stabilized Embedding Problem for Integral Ellipsoids
Dan Cristofaro-Gardiner, Richard Hind, Kyler Siegel
The third named author has been developing a theory of "higher" symplectic capacities. These capacities are invariant under taking products, and so are well-suited for studying the…
Special eccentricities of rational four-dimensional ellipsoids
Dan Cristofaro-Gardiner
A striking result of McDuff and Schlenk asserts that in determining when a four-dimensional symplectic ellipsoid can be symplectically embedded into a four-dimensional symplectic b…
On infinite staircases in toric symplectic four-manifolds
Dan Cristofaro-Gardiner, Tara S. Holm, Alessia Mandini +1
An influential result of McDuff and Schlenk asserts that the function that encodes when a four-dimensional symplectic ellipsoid can be embedded into a four-dimensional ball has a r…
Proof of the simplicity conjecture
Dan Cristofaro-Gardiner, Vincent Humilière, Sobhan Seyfaddini
In the 1970s, Fathi, having proven that the group of compactly supported volume-preserving homeomorphisms of the -ball is simple for , asked if the same statement holds…
The action spectrum characterizes closed contact 3-manifolds all of whose Reeb orbits are closed
Daniel Cristofaro-Gardiner, Marco Mazzucchelli
A classical theorem due to Wadsley implies that, on a connected contact manifold all of whose Reeb orbits are closed, there is a common period for the Reeb orbits. In this paper we…
Sub-leading asymptotics of ECH capacities
Daniel Cristofaro-Gardiner, Nikhil Savale
In previous work, the first author and collaborators showed that the leading asymptotics of the embedded contact homology (ECH) spectrum recovers the contact volume. Our main theor…
The ghost stairs stabilize to sharp symplectic embedding obstructions
Dan Cristofaro-Gardiner, Richard Hind, Dusa McDuff
In determining when a four-dimensional ellipsoid can be symplectically embedded into a ball, McDuff and Schlenk found an infinite sequence of "ghost" obstructions that generate an…
Torsion contact forms in three dimensions have two or infinitely many Reeb orbits
Dan Cristofaro-Gardiner, Michael Hutchings, Dan Pomerleano
We prove that every nondegenerate contact form on a closed connected three-manifold, such that the associated contact structure has torsion first Chern class, has either two or inf…
Symplectic embeddings of four-dimensional ellipsoids into integral polydiscs
Daniel Cristofaro-Gardiner, David Frenkel, Felix Schlenk
In previous work, the second author and Müller determined the function giving the smallest dilate of the polydisc into which the ellipsoid symplectically e…
Symplectic embeddings of products
D. Cristofaro-Gardiner, R. Hind
McDuff and Schlenk determined when a four-dimensional ellipsoid can be symplectically embedded into a four-dimensional ball, and found that when the ellipsoid is close to round, th…