arXiv research

Study proves rigid spectral properties of planets with metric discontinuities.

As early as 1972, Penrose - in a purely formal way - introduced a "discontinuous coordinate transformation", which relates a continuous representation of the metric of impulsive pp-waves to a discontinuous one. On the basis of the invertibility concept for generalized functions developed recently by the first author, w…

Metric WPD for pseudo-Anosov maps shows many unbounded quasi-morphisms.

A new geometry for comparing signals, overcoming traditional limitations.

The paper connects geometric and topological concepts to bound distances between metric spaces.

Extends index theorem to domain walls with discontinuous Riemannian connections.

To study the regularity of heat flow, Lin-Wang[1] introduced the quasi-harmonic sphere, which is a harmonic map from $M=(\mathbb{R}^m,e^{-\frac{|x|^2}{2(m-2)}}ds_0^2)$ to $N$ with finite energy. Here $ds_0^2$ is Euclidean metric in $\mathbb{R}^m$. Ding-Zhao [2] showed that if the target is a sphere, any equivariant qua…

Every lattice H in a connected semi-simple Lie group G acts properly discontinuously by isometries on the contractible manifold G/K (K a maximal compact subgroup of G). We prove that if H acts on a contractible manifold W and if either 1) the action is properly discontinuous, or 2) W is equipped with a complete Riemann…

We first analyze the integrated density of states (IDS) of periodic Schrödinger operators on an amenable covering manifold. A criterion for the continuity of the IDS at a prescribed energy is given along with examples of operators with both continuous and discontinuous IDS'. Subsequently, alloy-type perturbations of th…

Proves nonemptyness of domains for specific group actions.

The study examines non-continuous Riemannian metrics on manifolds and their infinitesimal properties.

Whenever a finitely generated group $G$ acts properly discontinuously by isometries on a metric space $X$, there is an induced uniform embedding (a Lipschitz and uniformly proper map) $ρ: G \rightarrow X$ given by mapping $G$ to an orbit. We study when there is a difference between a finitely generated group $G$ acting…

Properly discontinuous actions of a surface group by affine automorphisms of $\mathbb R^d$ were shown to exist by Danciger-Gueritaud-Kassel. We show, however, that if the linear part of an affine surface group action is in the Hitchin component, then the action fails to be properly discontinuous. The key case is that o…

We consider the deformation of a discontinuous group acting on the Euclidean space by affine transformations. A distinguished feature here is that even a `small' deformation of a discrete subgroup may destroy proper discontinuity of its action. In order to understand the local structure of the deformation space of disc…

Cut-DeepONet handles discontinuities and sharp transitions in neural operators.

Study proves existence of equilibrium in incomplete economies with discontinuous volatility.

New domains of discontinuity found for Anosov representations.

Study the discontinuity of functions not embeddable in Euclidean space.

Study new symmetries in non-symmetric spaces and discontinuous groups.

Paper finds surface groups can deform in reductive symmetric spaces.

A new method for unsupervised disentanglement using axis-aligned cliffs.

New insights into the geometry of flows on 3-manifolds.

New method estimates active subspaces for jump-discontinuous functions.

This article gives an up-to-date account of the theory of discrete group actions on non-Riemannian homogeneous spaces. As an introduction of the motifs of this article, we begin by reviewing the current knowledge of possible global forms of pseudo-Riemannian manifolds with constant curvatures, and discuss what kind of …

The first known example of a complete Riemannian manifold whose isoperimetric profile is discontinuous is given.

Paper analyzes error in stochastic approximation for discontinuous functions.

Bayesian emulator tackles models with discontinuities efficiently.

Study stabilizes representations of hyperbolic groups, finding new characterizations.

We characterise completely when limit sets, as parametrised by Cannon-Thurston maps, move discontinuously for a sequence of algebraically convergent quasi-Fuchsian groups.

We show that there is a complete connected 2-dimensional Riemannian manifold with discontinuous isoperimetric profile, answering a question of Nardulli and Pansu.

Volunteer labor can temporarily yield lower benefits to charities than its costs. In such instances, organizations may wish to defer volunteer donations to a later date. Exploiting a discontinuity in blood donations' eligibility criteria, we show that deferring donors reduces their future volunteerism. In our setting, …

The paper is a study of geodesic in two-dimensional pseudo-Riemannian metrics. Firstly, the local properties of geodesics in a neighborhood of generic parabolic points are investigated. The equation of the geodesic flow has singularities at such points that leads to a curious phenomenon: geodesics cannot pass through s…

We develop a general term structure framework taking stochastic discontinuities explicitly into account. Stochastic discontinuities are a key feature in interest rate markets, as for example the jumps of the term structures in correspondence to monetary policy meetings of the ECB show. We provide a general analysis of …

Counterexample disproves Borde-Sorkin conjecture on causal continuity of Morse spacetimes.

In this paper, we present a method for the accurate estimation of the derivative (aka.~sensitivity) of expectations of functions involving an indicator function by combining a stochastic algorithmic differentiation and a regression. The method is an improvement of the approach presented in [Risk Magazine April 2018]. T…

We study the properly discontinuous and isometric actions on the unit sphere of infinite dimensional Hilbert spaces and we get some new examples of Hilbert manifold with costant positive sectional curvature. We prove some necessary conditions for a group to act isometrically and properly discontinuously and in the case…

This work models overnight rates with jumps and discontinuities, extending classical short-rate models.

We give a geometric interpretation of the maximal Satake compactification of symmetric spaces $X=G/K$ of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable $G$-invariant Finsler metric on $X$. As an application, we establish the existence of natural bordifications, as orbifold…

Quasi-experimental research designs, such as regression discontinuity and interrupted time series, allow for causal inference in the absence of a randomized controlled trial, at the cost of additional assumptions. In this paper, we provide a framework for discontinuity-based designs using Bayesian model comparison and …

The study explores deformations of discrete subgroups in non-compact homogeneous spaces.

We find a canonical decomposition of a geodesic current on a surface of finite type arising from a topological decomposition of the surface along special geodesics. We show that each component either is associated to a measured lamination or has positive systole. For a current with positive systole, we show that the in…

Paper analyzes SGHMC for non-convex optimization with discontinuous gradients.

SGD learns sparse parities near computational limits with discontinuous phase transitions.

This paper tackles discontinuous neural networks for better approximation of piecewise continuous functions.

In the present paper, we prove that no infinite group acts isometrically, effectively, and properly discontinuously on a certain class of Lorentzian manifolds that are not necessarily homogeneous.

Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.

In this article we study properly discontinuous actions on Hilbert manifolds giving new examples of complete Hilbert manifolds with nonnegative, respectively nonpositive, sectional curvature with infinite fundamental group. We also get examples of complete infinite dimensional Kähler manifolds with positive holomorphic…

This article contains a detailed study, in the toric case, of the test configuration geodesic rays defined by Phong-Sturm. We show that the `Bergman approximations' of Phong-Sturm converge in C^1 to the geodesic ray and that the geodesic ray itself is C^{1,1} and no better. The \kahler metrics associated to the geodesi…