arXiv research

Study on pairwise counter-monotonicity, a type of negative dependence.

The paper explores the relationship between joint mixability and negative dependence structures.

The paper finds optimal threshold strategies for insurance companies with a positive terminal value at creeping ruin.

Develops thermodynamic formalism for quasimorphisms on negatively curved spaces.

The paper constructs metrics with non-negative curvature and harmonic maps.

Motivated by the study of Killing forms on compact Riemannian manifolds of negative sectional curvature, we introduce the notion of generalized vector cross products on $\mathbb{R}^n$ and give their classification. Using previous results about Killing tensors on negatively curved manifolds and a new characterization of…

Study on prescribing curvature on specific manifolds with negative Gauduchon degree.

The method integrates survival constraints into NMF for identifying survival-associated gene clusters.

We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path connected; and, moreover, that the associated moduli space (i.e., modulo orientation-preserving diffeomorphisms of the three-ball) is contractible. As an application, using resul…

We prove $R$-bisectoriality and boundedness of the $H^\infty$-functional calculus in $L^p$ for all $1<p<\infty$ for the Hodge-Dirac operator associated with Witten Laplacians on complete Riemannian manifolds with non-negative Bakry-Emery Ricci curvature on $k$-forms.

News novelty predicts negative stock market returns.

This paper explores the relation between the structure of fibre bundles akin to those associated to a closed almost nonnegatively sectionally curved manifold and rational homotopy theory.

Model learns image-word associations from captions using contrastive learning.

Given an associative 3-fold in R^7 which is asymptotically conical with generic rate less than 1, we show that its moduli space of deformations is locally homeomorphic to the kernel of a smooth map between smooth manifolds. Moreover, the virtual dimension of the moduli space is computed and shown to be non-negative for…

A Steiner deltoid maintains constant area across all boundary points of an ellipse.

Paper proves rigidity of metrics near hyperbolic ones in 3D.

The entropy of minimal surfaces is minimized in hyperbolic manifolds.

This paper classifies minimal fillings of lens spaces.

Learning rates in stochastic neural network training are currently determined a priori to training, using expensive manual or automated iterative tuning. This study proposes gradient-only line searches to resolve the learning rate for neural network training algorithms. Stochastic sub-sampling during training decreases…

Social media based digital epidemiology has the potential to support faster response and deeper understanding of public health related threats. This study proposes a new framework to analyze unstructured health related textual data via Twitter users' post (tweets) to characterize the negative health sentiments and non-…

Let $(M,g)$ be a complete non-compact Riemannian manifold. We consider operators of the form $Δ_g + V$, where $Δ_g$ is the non-negative Laplacian associated with the metric $g$, and $V$ a locally integrable function. Let $ρ: (\hat{M},\hat{g}) \to (M,g)$ be a Riemannian covering, with Laplacian $Δ_{\hat{g}}$ and potenti…

Paper classifies fibers of fat Riemannian submersions with non-negative curvature.

We compute the log canonical thresholds of non-negatively curved singular hermitian metrics on ample linearized line bundles on bi-equivariant group compactifications of complex reductive groups. To this end, we associate to any such metric a convex function whose asymptotic behavior determines the log canonical thresh…

Investigates how ESG mandates affect portfolio efficiency and risk premia.

The paper solves curvature prescription on a disk with negative Gaussian curvature.

The main result presented here is that the flow associated with a riemannian metric and a non zero magnetic field on a compact oriented surface without boundary, under assumptions of hyperbolic type, cannot have the same length spectrum of topologically corresponding periodic orbits as the geodesic flow associated with…

We prove the existence of "half-plane differentials" with prescribed local data on any Riemann surface. These are meromorphic quadratic differentials with higher-order poles which have an associated singular flat metric isometric to a collection of euclidean half-planes glued by an interval-exchange map on their bounda…

We present a 2x2 Lax representation for discrete circular nets of constant negative Gauß curvature. It is tightly linked to the 4D consistency of the Lax representation of discrete K-nets (in asymptotic line parametrization). The description gives rise to Bäcklund transformations and an associated family. All the membe…

New proof shows surfaces can have identical length spectra but not simple ones.

We analyze an energy functional associated to Conformal Ricci Flow along closed manifolds with constant negative scalar curvature. Given initial conditions we use this functional to demonstrate the uniqueness of both the metric and the pressure function along Conformal Ricci Flow.

Physicists believe, with some justification, that there should be a correspondence between familiar properties of Newtonian gravity and properties of solutions of the Einstein equations. The Positive Mass Theorem (PMT), first proved over twenty years ago \cite{SchoenYau79b,Witten81}, is a remarkable testament to this f…

SOS programming verifies MTW tensor non-negativity for optimal transport maps.

Let $(M,g)$ be a closed oriented negatively curved surface. A unitary connection on a Hermitian vector bundle over $M$ is said to be transparent if its parallel transport along the closed geodesics of $g$ is the identity. We study the space of such connections modulo gauge and we prove a classification result in terms …

Lower bounds for eigenvalues on manifolds with negative Ricci curvature.

Common perpendiculars equidistribute in negatively curved spaces.

Geodesic currents in strongly hyperbolic spaces are dense.

Lower bounds for eigenvalues on manifolds with negative Ricci curvature.

We present a unified method of construction of surfaces associated with Grassmannian sigma models, expressed in terms of an orthogonal projector. This description leads to compact formulae for structural equations of two-dimensional surfaces immersed in the su(N) algebra. In the special case of the CP^1 sigma model we …

The paper generalizes a Steklov eigenvalue inequality for substatic triples under non-negative Ricci curvature.

For a compact riemannian manifold of negative curvature, the geodesic foliation of its unit tangent bundle is independent of the negatively curved metric, up to Holder bicontinuous homeomorphism. However, the riemannian metric defines a natural transverse measure to this foliation, the Liouville transverse measure, whi…

Assume that $M(\mathcal{T})$ is a rational homology sphere plumbed 3-manifold associated with a connected negative definite graph $\mathcal{T}$. We consider the combinatorial multivariable Poincaré series associated with $\mathcal{T}$ and its counting functions, which encode rich topological information. Using the `per…

The paper studies metrics on vector bundles with singularities and their associated forms.

This paper examines SVB's failure and its impact on bank stocks.

By adapting some ideas of M. Ledoux \cite{ledoux2}, \cite{ledoux-stflour} and \cite{Led} to a sub-Riemannian framework we study Sobolev, Poincaré and isoperimetric inequalities associated to subelliptic diffusion operators that satisfy the generalized curvature dimension inequality that was introduced by F. Baudoin and…

Proves cup product homomorphism for bounded cohomology on negatively curved manifolds.

In this note, we study the dynamics and associated zeta functions of conformally compact manifolds with variable negative sectional curvatures. We begin with a discussion of a larger class of manifolds known as convex co-compact manifolds with variable negative curvature. Applying results from dynamics on these spaces,…

We introduce the concept of "negative bubbles" as the mirror image of standard financial bubbles, in which positive feedback mechanisms may lead to transient accelerating price falls. To model these negative bubbles, we adapt the Johansen-Ledoit-Sornette (JLS) model of rational expectation bubbles with a hazard rate de…

This paper shows moduli spaces of RCD(0,2) structures are contractible.