arXiv research

Improved volume estimates for right-angled polyhedra in hyperbolic space.

Characterizes stable minimal capillary surfaces with specific angles.

Several dihedral angles prediction methods were developed for protein structure prediction and their other applications. However, distribution of predicted angles would not be similar to that of real angles. To address this we employed generative adversarial networks (GAN). Generative adversarial networks are composed …

Study calibrates high-dimensional binary classifiers using angle between estimator and true weights.

We prove that capillary surfaces converge to a specific energy density as the angle approaches zero.

New method estimates intrinsic dimensionality using angles, not distances.

Quantifies closeness of special Lagrangians under Floer conditions.

Improved estimates for singularities in capillary surfaces.

For data living in a manifold $M\subseteq \mathbb{R}^m$ and a point $p\in M$ we consider a statistic $U_{k,n}$ which estimates the variance of the angle between pairs of vectors $X_i-p$ and $X_j-p$, for data points $X_i$, $X_j$, near $p$, and evaluate this statistic as a tool for estimation of the intrinsic dimension o…

We study the prescribed mean curvature equation with a prescribed boundary contact angle condition in $M\times\R$ where $M^n$ is a Riemannian submanifold in $\R^{n+1}$. The main purpose is to establish a priori gradient estimates for solutions, from which the long time existence of the solution are derived.

In his paper "On the Schlafli differential equality", J. Milnor conjectured that the volume of n-dimensional hyperbolic and spherical simplices, as a function of the dihedral angles, extends continuously to the closure of the space of allowable angles (``The continuity conjecture''), and furthermore, the limit at a bou…

Dynamic angles estimated from noisy measurements over time with smoothness constraints.

Paper tackles joint community detection and phase synchronization in stochastic block models.

The problem of estimating the number of sources and their angles of arrival from a single antenna array observation has been an active area of research in the signal processing community for the last few decades. When the number of sources is large, the maximum likelihood estimator is intractable due to its very high c…

In this letter, we consider two sets of observations defined as subspace signals embedded in noise and we wish to analyze the distance between these two subspaces. The latter entails evaluating the angles between the subspaces, an issue reminiscent of the well-known Procrustes problem. A Bayesian approach is investigat…

ANGLE tackles circular data regression, improving predictive performance.

We prove an optimal systolic inequality for nonpositively curved Dyck's surfaces. The extremal surface is flat with eight conical singularities, six of angle theta and two of angle 9pi - theta, for a suitable theta with cos(theta) in Q(sqrt{19}). Relying on some delicate capacity estimates, we also show that the extrem…

New method uses neural networks for accurate angle estimation in noisy conditions.

Defines Kahler angle for a broader context.

We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant complex angle with respect to a fixed spacelike plane. This notion is the natural Lo…

Study angle structures on pseudo 3-manifolds, proving existence for some cases.

In this paper we study the right-angled Coxeter groups that acts geometrically on the Salvetti complex of a certain right-angled Artin group, which we refer to as Croke-Kleiner spaces. We prove that any right-angled Coxeter group that acts geometrically on the Croke-Kleiner spaces acts with $π/2$ angles between reflect…

We prove that on one Kähler-Einstein Fano manifold without holomorphic vector fields, there exists a unique conical Kähler-Einstein metric along a simple normal crossing divisor with admissible prescribed cone angles. We also establish a curvature estimate for conic metrics along a simple normal crossing divisor which …

Develops a novel approach for estimating optimal DTRs with multicategory treatments and censored data.

Introduces a new geometry based on difference angles, showing unique properties.

To a knot in 3-space, one can associate a sequence of Laurent polynomials, whose $n$th term is the $n$th colored Jones polynomial. The Volume Conjecture for small angles states that the value of the $n$-th colored Jones polynomial at $e^{\a/n}$ is a sequence of complex numbers that grows subexponentially, for a fixed s…

Stiefel-Whitney classes of moment-angle manifolds are trivial.

In this paper, we discuss the Lagrangian angle and the Kähler angle of immersed surfaces in $\mathbb C^2$. Firstly, we provide an extension of Lagrangian angle, Maslov form and Maslov class to more general surfaces in $\mathbb C^2$ than Lagrangian surfaces, and then naturally extend a theorem by J.-M. Morvan to surface…

New framework for inference with LAR, explaining variable contributions and providing stopping rules.

Uniqueness of quasi-roots explored in right-angled Artin groups.

We demonstrate how to construct three-dimensional compact hyperbolic polyhedra using Newton's Method. Under the restriction that the dihedral angles are non-obtuse, Andreev's Theorem provides as necessary and sufficient conditions five classes of linear inequalities for the dihedral angles of a compact hyperbolic polyh…

In the last decades the estimation of the intrinsic dimensionality of a dataset has gained considerable importance. Despite the great deal of research work devoted to this task, most of the proposed solutions prove to be unreliable when the intrinsic dimensionality of the input dataset is high and the manifold where th…

This note generalizes the visual angle to convex sets in 3D space.

Study proves existence of weak mean curvature flow with contact angle.

This paper explores historical and philosophical aspects of angles and solid angles, inspired by Euler's work.

Real moment-angle manifolds of combinatorially equivalent simple polytopes are equivariantly diffeomorphic.

An equiangular hyperbolic Coxeter polyhedron is a hyperbolic polyhedron where all dihedral angles are equal to π/n for some fixed integer n at least 2. It is a consequence of Andreev's theorem that either n=3 and the polyhedron has all ideal vertices or that n=2. Volume estimates are given for all equiangular hyperboli…

Agol recently introduced the notion of a veering triangulation, and showed that such triangulations naturally arise as layered triangulations of fibered hyperbolic 3-manifolds. We prove, by a constructive argument, that every veering triangulation admits positive angle structures, recovering a result of Hodgson, Rubins…

We provide a congruence theorem for minimal surfaces in $S^5$ with constant contact angle using Gauss-Codazzi-Ricci equations. More precisely, we prove that Gauss-Codazzi-Ricci equations for minimal surfaces in $S^5$ with constant contact angle satisfy an equation for the Laplacian of the holomorphic angle. Also, we wi…

Moment-angle manifolds provide a wide class of examples of non-Kaehler compact complex manifolds. A complex moment-angle manifold Z is constructed via certain combinatorial data, called a complete simplicial fan. In the case of rational fans, the manifold Z is the total space of a holomorphic bundle over a toric variet…

Surveying connections between graph combinatorics and algebraic right-angled Artin groups.

Study minimal hypersurfaces in manifolds with bounded Ricci curvature.

We give a new notion of angle in general metric spaces; more precisely, given a triple a points $p,x,q$ in a metric space $(X,d)$, we introduce the notion of angle cone ${\angle_{pxq}}$ as being an interval ${\angle_{pxq}}:=[\angle^-_{pxq},\angle^+_{pxq}]$, where the quantities $\angle^\pm_{pxq}$ are defined in terms o…

The paper studies prescribed angle surfaces in Riemannian manifolds with torse-forming vector fields.

In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle property. Moreover, the natural extension to normal and binormal constant angle sur…

We survey the role of right-angled Artin groups in the theory of diffeomorphism groups of low dimensional manifolds. We first describe some of the subgroup structure of right-angled Artin groups. We then discuss the interplay between algebraic structure, compactness, and regularity for group actions on one--dimensional…

Study on null hypersurfaces with constant angle in Lorentzian manifolds.

Estimates for scalar curvature equations on Kähler manifolds with singularities.