Related papers: Lorentzian distance functions in contact geometry

Distance function is a main metrics of measuring the affinity between two data points in machine learning. Extant distance functions often provide unreachable distance values in real applications. This can lead to incorrect measure of the…

We study locally conformally homogeneous Lorentzian manifolds of dimension at least $3$, admitting an essential pseudo-group of local conformal transformations. Generalizing a recent result of Alekseevsky and Galaev, we show that any such…

We show that there exist contact isotopies of the standard contact sphere whose time-1 maps do not have any translated points which are optimally close to the identity in the Shelukhin-Hofer distance. This proves the sharpness of a theorem…

We prove that all functions obeying the Kramers-Kronig relations can be approximated as superpositions of Lorentzian functions, to any precision. As a result, the typical text-book analysis of dielectric dispersion response functions in…

In the first part of the paper, we study conformal groups that act properly discontinuously and cocompactly on simply connected, non-flat homogeneous plane waves. We show that proper cocompact similarity actions that are not isometric can…

We construct a natural prequantization space over a monotone product of a toric manifold and an arbitrary number of complex Grassmannians of 2-planes in even-dimensional complex spaces, and prove that the universal cover of the identity…

We prove a H\"older-type inequality for the Hausdorff distance between Lagrangians with respect to the Lagrangian spectral distance or the Hofer-Chekanov distance in the spirit of Joksimovi\'c-Seyfaddini [arXiv:2207.11813]. This inequality…

We introduce conformal transformations in the synthetic setting of metric spaces and Lorentzian (pre-)length spaces. Our main focus lies on the Lorentzian case, where, motivated by the need to extend classical notions to spaces of low…

In this paper we study the local linearization of the Hellinger--Kantorovich distance via its Riemannian structure. We give explicit expressions for the logarithmic and exponential map and identify a suitable notion of a Riemannian inner…

We prove that every Kaehler metric, whose potential is a function of the time-like distance in the flat Kaehler-Lorentz space, is of quasi-constant holomorphic sectional curvatures, satisfying certain conditions. This gives a local…

The defining property of every three-dimensional $\varepsilon$-contact manifold is shown to be equivalent to requiring the fulfillment of London's equation in 2+1 electromagnetism. To illustrate this point, we show that every such manifold…

We determine the contact mapping class group of the standard contact structures on lens spaces. To prove the main result, we use the one-parametric convex surface theory to classify Legendrian and transverse rational unknots in any tight…

For certain contact manifolds admitting a 1-periodic Reeb flow we construct a conjugation-invariant norm on the universal cover of the contactomorphism group. With respect to this norm the group admits a quasi-isometric monomorphism of the…

We study a number of questions related to the $C^0$-topology of contactomorphisms and contact homeomorphisms. In particular, we show a connection between Rokhlin property of contact homeomorphisms and contact non-squeezing, we define a new…

Timelike Liouville field theory is a candidate model for positive curvature two-dimensional quantum gravity, but a mathematically controlled Lorentzian formulation has remained elusive. In this paper we construct the theory on the cylinder…

Lavrentiev curves form a special class of rectifiable curves which includes cusp-free piecewise smooth curves. We call a Lavrentiev curve Legendrian if the integral of the contact form equals zero on any its subarc. We define Legendrian…

We consider collections of Lagrangian submanifolds of a given symplectic manifold which respect uniform bounds of curvature type coming from an auxiliary Riemannian metric. We prove that, for a large class of metrics on these collections,…

We introduce a persistence-like pseudo-distance on Tamarkin's category and prove that the distance between an object and its Hamiltonian deformation is at most the Hofer norm of the Hamiltonian function. Using the distance, we show a…

The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold $M$ with the Grothendieck group of constructible sheaves on $M$. When $M$ is a finite dimensional real vector space,…

In Persistent Homology and Topology, filtrations are usually given by introducing an ordered collection of sets or a continuous function from a topological space to $\R^n$. A natural question arises, whether these approaches are equivalent…