2 citations · 3 across the 9 of their papers we have counts for
9 papers
Bordism classes of loops and Floer's equation in cotangent bundles
Filip Broćić, Dylan Cant
For each representative of a bordism class in the free loop space of a manifold, we associate a moduli space of finite length Floer cylinders in the cotangent bundle…
Adiabatic compactness for holomorphic curves with boundary on nearby Lagrangians
Dylan Cant, Daren Chen
In his 1989 paper, Floer established a connection between holomorphic strips with boundary on a Lagrangian and a small Hamiltonian push-off , and gradient flow lines for…
Remarks on the oscillation energy of Legendrian isotopies
Dylan Cant
We construct non-compact contact manifolds containing compact Legendrians which can be displaced from their Reeb flow with arbitrarily small oscillation energy. We use this to show…
Contact non-squeezing and orderability via the shape invariant
Dylan Cant
We prove a contact non-squeezing result for a class of embeddings between starshaped domains in the contactization of the symplectization of the unit cotangent bundle of certain ma…
Contactomorphisms of the sphere without translated points
Dylan Cant
We construct a contactomorphism of the standard sphere which does not have any translated points, providing a negative answer to a conjecture posed by Sandon.
An Index Formula for Cauchy-Riemann Operators on Surfaces with Boundary Punctures
Dylan Cant
We give a self-contained proof of a formula computing the Fredholm index for asymptotically non-degenerate Cauchy-Riemann operators on surfaces with boundary punctures using the me…
Perturbed Holomorphic Cylinders, Exponential Estimates, and Flow Lines
Dylan Cant
A convergence result for perturbed holomorphic cylinders in is proved; a sequence of perturbed holomorphic cylinders converges to a configuration of two holomorph…
Exponential Convergence to Non-degenerate Reeb Chords
Dylan Cant
Exponential convergence type results are proved for holomorphic curves in the symplectization of a contact manifold with boundary on a Legendrian cylinder. The results are prov…
A Curvature Flow and Applications to an Isoperimetric Inequality
Dylan Cant
Long time existence and convergence to a circle is proved for radial graph solutions to a mean curvature type curve flow in warped product surfaces (under a weak assumption on the…