A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Extends Gromov non-squeezing to locally conformally symplectic structures.
Study non-squeezing phenomena in contact geometry using specific capacities.
The paper extends Gromov's non-squeezing theorem to deformed symplectic forms.
Improved non-squeezing theorem for calibrated geometries proved.
Two new proofs of Gromov's non-squeezing theorem using curve reparametrization and gradient bounds.
Starting from the work of Bhupal, we extend to the contact case the Viterbo capacity and Traynor's construction of symplectic homology. As an application we get a new proof of the Non-Squeezing Theorem of Eliashberg, Kim and Polterovich.
The study explores pinwheels in symplectic surfaces and non-squeezing of rational homology balls.
The paper quantifies how much of a 4-ball must be removed to squeeze into a cylinder, proving a lower bound on the Minkowski dimension.
New methods prove non-squeezing in locally conformal symplectic geometry.
Contact squeezing prevented in certain prequantized balls via generating functions.
Contact Lie systems analyze integral curves of Hamiltonian vector fields.
We prove that if the unit codisc bundle of a closed Riemannian manifold embeds symplectically into a symplectic cylinder of radius one then the length of the shortest nontrivial closed geodesic is at most half the area of the unit disc.
The paper recovers contact forms from boundary data using vector fields and Lyapunov functions.
In her PhD thesis Milin developed an equivariant version of the contact homology groups constructed by Eliashberg, Kim and Polterovich and used it to prove an equivariant contact non-squeezing theorem. In this article we re-obtain the same result in the setting of generating functions, starting from the homology groups…
We initiate here the study of Gromov-Witten theory of locally conformally symplectic manifolds or $\lcs$ manifolds, $\lcsm$'s for short, which are a natural generalization of both contact and symplectic manifolds. We find that the main new phenomenon (relative to the symplectic case) is the potential existence of holom…
We prove a coisotropic intersection result and deduce the following: 1. Lower bounds on the displacement energy of a subset of a symplectic manifold, in particular a sharp stable energy-Gromov-width inequality. 2. A stable non-squeezing result for neighborhoods of products of unit spheres. 3. Existence of a "badly sque…
Contact manifolds are odd-dimensional smooth manifolds endowed with a maximally non-integrable field of hyperplanes. They are intimately related to symplectic manifolds, i.e. even-dimensional smooth manifolds endowed with a closed non-degenerate 2-form. Although in symplectic topology a famous bi-invariant metric, the …
The systolic ratio of a contact form on the three-sphere is the quantity \[ ρ_{\mathrm{sys}}(α) = \frac{T_{\min}(α)^2}{\mathrm{vol}(S^3,α\wedge dα)}, \] where is the minimal period of closed Reeb orbits on . A Zoll contact form is a contact form such that all the orbits of the corresponding R…
Nearby pinwheels are isotopic, solving Arnold's conjecture.
In this paper we consider a geometric variant of Hofer's symplectic energy, which was first considered by Eliashberg and Hofer in connection with their study of the extent to which the interior of a region in a symplectic manifold determines its boundary. We prove, by a simple geometric argument, that both versions of …
In this paper we first show that the necessary condition introduced in our previous paper is also a sufficient condition for a path to be a geodesic in the group $\Ham^c(M)$ of compactly supported Hamiltonian symplectomorphisms. This applies with no restriction on . We then discuss conditions which guarantee that su…