arXiv research

Calegari, Marques, and Neves count minimal surfaces in hyperbolic manifolds.

We define a laminar branched surface to be a branched surface satisfying the following conditions: (1) Its horizontal boundary is incompressible; (2) there is no monogon; (3) there is no Reeb component; (4) there is no sink disk (after eliminating trivial bubbles in the branched surface). The first three conditions are…

Thurston showed that the fundamental group of a close atoroidal 3-manifold admitting a co-oriented taut foliation acts faithfully on the circle by orientation-preserving homeomorphisms. This action on the circle is called a universal circle action due to its rich information. In this article, we first review Thurston's…

We define sink marks for branched complexes and find conditions for them to determine a branched surface structure. These will be used to construct branched surfaces in knot and tangle complements. We will extend Delman's theorem and prove that a Montesinos knot $K$ of length at least 3 has a persistently laminar branc…

We show that on a Riemann surface lamination locally embedded in $\mathbb{C}^2$, $C^1$ functions (in the sense of the $C^1$ structure of the lamination) are uniform limits of ambient $C^1$ functions, with $L^p$ control on the derivatives along the leaves. This implies that locally in $C^2$, a (1,1) positive closed curr…

Study shows automorphisms of Markov surfaces share periodic points if they share a common iterate.

In this paper, we show the existence of real-analytic stationary Navier-Stokes flows with isotropic streamlines in all latitudes in some simply-connected flow region on a rotating round sphere. We also exclude the possibility of having a Poiseuille's flow profile to be one of these stationary Navier-Stokes flows with i…

We show that there are algorithms to determine if a 3-manifold contains an essential lamination or a Reebless foliation.

Self-organized criticality has been claimed to play an important role in many natural and social systems. In the present work we empirically investigate the relevance of this theory to stock-market dynamics. Avalanches in stock-market indices are identified using a multi-scale wavelet-filtering analysis designed to rem…

The Stock Market is a complex self-interacting system, characterized by an intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically about the possibility that the market is in a self-organized critical state (SOC). A wavelet transform metho…

Minimal surfaces and average area ratio found to be maximized by hyperbolic metrics.

A persistent lamination for a knot K is an essential lamination in the complement of the K, which remains essential after every non-trivial Dehn surgery along K. In particular, this implies that all of the Dehn surgery manifolds have universal cover R^3. This paper presents a method for building tangles T with the prop…

We analyse the existence question for essential laminations in 3-manifolds. The purpose is to prove that there are infinitely many closed hyperbolic 3-manifolds which do not admit essential laminations. This answers in the negative a question posed by Gabai and Oertel. The proof is obtained by analysing certain group a…

In agreement with the recent research findings in the econophysics, we propose that the nonlinear dynamic chaos can be generated by the turbulent capital flows in both the quantitative easing transmission channels and the transaction networks channels, when there are the laminar turbulent capital flows transitions in t…

Whether every hyperbolic 3-manifold admits a tight contact structure or not is an open question. Many hyperbolic 3-manifolds contain taut foliations and taut foliations can be perturbed to tight contact structures. The first examples of hyperbolic 3-manifolds without taut foliations were constructed by Roberts, Sharesh…

Following previous work of the second author, we establish more properties of groups of circle homeomorphisms which admit invariant laminations. In this paper, we focus on a certain type of such groups-so-called pseudo-fibered groups, and show that many 3-manifold groups are examples of pseudo-fibered groups. We then p…

New method shows how certain groups act on 3-orbifolds.

Paper applies fluid dynamics to stock market behavior.

This paper characterizes Fuchsian groups acting on the circle with invariant laminations.

Detect slopes in toroidal 3-manifolds to prove properties of fundamental groups.

Paper tackles $L$-space conjecture for knot manifolds, proving equivalence for some properties.

Compact models for methane/air combustion reduce complexity without sacrificing accuracy.

Study invariant measures on measured laminations for subgroups of mapping class group.

New set-valued star-shaped risk measures introduced for better risk assessment.

The Bergman measure converges to the Zhang measure on a hybrid space.

Bayesian approach to robust risk measures under model uncertainty.

Introduces Star-Shaped deviation measures for risk analysis.

The paper studies dynamic star-shaped risk measures and their representation.

Transformers can interpolate between arbitrary measures.

Classifies invariant measures on specific character varieties.

Paper characterizes star-shaped risk measures and their properties.

Paper introduces quasi-logconvex risk measures and their properties.

Submodularity is studied for convex risk measures, including Expected Shortfall.

New geometric measure simplifies complex analysis.

The paper explores non-convex risk measures and their characterizations.

The paper calculates extreme measures in continuous time conic finance.

One often finds in the literature connections between measures of fairness and measures of feature importance employed to interpret trained classifiers. However, there seems to be no study that compares fairness measures and feature importance measures. In this paper we propose ways to evaluate and compare such measure…

Paper characterizes monotonic mean-deviation risk measures.

Dual representations for robust risk measures and uncertainty sets.

Introduces factor risk measures to assess risk relative to multiple factors.

A scalable approach to learning from probability measures using quantization.

Study on measurable pseudo-Anosov maps on surfaces.

In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework for considering not only the target physical model but also the measurement model…

Risk measures for multivariate financial positions are studied in a utility-based framework. Under a certain incomplete preference relation, shortfall and divergence risk measures are defined as the optimal values of specific set minimization problems. The dual relationship between these two classes of multivariate ris…

The Cannon-Thurston map's pushed measures on the circle are singular with respect to sphere measures.

New weighted surface area measures for convex bodies with applications.

Standardized fairness measures for continuous risk scores using Wasserstein distance.

Starting with the work of Preiss on the geometry of measures, the classification of uniform measures in $\mathbb R^d$ has remained open, except for $d=1$ and for compactly supported measures in $d=2$, and for codimension $1$. In this paper we study $1$-dimensional measures in $\mathbb R^d$ for all $d$ and classify unif…