arXiv research

The study proves poor ideal three-edge triangulations are minimal for certain 3-manifolds.

We give a simple method to find ideal points of the character variety of a 3-manifold from an ideal triangulation.

Short proof for ideal polygons with near optimal orthogeodesic decomposition.

A method uses CG to create efficient channels for ideal observers.

The goal of this work is to study the ideals of the Goldman Lie algebra $S$. To do so, we construct an algebra homomorphism from $S$ to a simpler algebraic structure, and focus on finding ideals of this new structure instead. The structure $S$ can be regarded as either a $\mathbb{Q}$-module or a $\mathbb{Q}$-module gen…

We investigate the rigidity of hyperbolic cone metrics on $3$-manifolds which are isometric gluing of ideal and hyper-ideal tetrahedra in hyperbolic spaces. These metrics will be called ideal and hyper-ideal hyperbolic polyhedral metrics. It is shown that a hyper-ideal hyperbolic polyhedral metric is determined up to i…

Defines timelike ideal boundary for non-positively curved Lorentzian spaces.

A taut ideal triangulation of a 3-manifold is a topological ideal triangulation with extra combinatorial structure: a choice of transverse orientation on each ideal 2-simplex, satisfying two simple conditions. The aim of this paper is to demonstrate that taut ideal triangulations are very common, and that their behavio…

The paper studies dynamical properties in semigroups modulo ideals.

We define the ideal simplicial volume for compact manifolds with boundary. Roughly speaking, the ideal simplicial volume of a manifold $M$ measures the minimal size of possibly ideal triangulations of $M$ "with real coefficients", thus providing a variation of the ordinary simplicial volume defined by Gromov in 1982, t…

The notion of ideal immersions was introduced by the author in 1990s. Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is a nice isometric immersion which produces the least possible amount of tension from the ambient space at each point. In this paper, we classify all ideal hypersur…

New formula calculates volumes of ideal hyperbolic drums.

Study of combinatorial Calabi flow on ideal circle patterns.

A biconservative submanifold of a Riemannian manifold is a sub- manifold with divergence free stress-energy tensor with respect to bienergy. These are generalizations of biharamonic submanifolds. In 2013, B. Y. Chen and M.I. Munteanu proved that $δ(2)$-ideal and $δ(3)$-ideal biharmonic hypersurfaces in Euclidean space …

The paper studies deformations of Lie ideals in Lie algebras.

Paper solves long-standing problem of infinite ideal polyhedra in hyperbolic space.

Wintgen ideal surfaces in E^4 form an important family of surfaces, namely surfaces with circular ellipse of curvature. Obviously, Wintgen ideal surfaces satisfy the pointwise equality K+K_N=H^2. In the present study we consider the Wintgen ideal surfaces in n-dimensional Euclidean space E^4. We have shown that Wintgen…

We discuss two different in general natural approaches to the ideal closure and ideal boundary of Busemann nonpositively curved metric space. It is shown that the identity map of the space admits surjective continuation from its coarse ideal closure to the weak one. We consider some situations when these closures coinc…

In this paper we provide a new obstruction to 0-concordance of knotted surfaces in $S^4$ in terms of Alexander ideals. We use this to prove the existence of infinitely many linearly independent 0-concordance classes and to provide the first proof that the submonoid of 2-knots is not a group. The main result is that the…

Combinatorial description of 3-manifolds using ordered triangulations.

Proof of existence for ideal triangulations that normalize fibers in certain 3-manifolds.

Every biharmonic Wintgen ideal submanifold in a Riemannian manifold of constant sectional curvature is either minimal or has constant mean curvature.

Study on Hermitian metrics on Lie algebras with specific ideals.

TBIP uses texts to quantify lawmakers' political positions.

The notion of ideal embeddings was introduced in [B.-Y. Chen, {Strings of Riemannian invariants, inequalities, ideal immersions and their applications.} The Third Pacific Rim Geometry Conference (Seoul, 1996), 7-60, Int. Press, Cambridge, MA, 1998]. Roughly speaking, an ideal embedding (or a best of living) is an isome…

We generalise work of Young-Eun Choi to the setting of ideal triangulations with vertex links of arbitrary genus, showing that the set of all (possibly incomplete) hyperbolic cone-manifold structures realised by positively oriented hyperbolic ideal tetrahedra on a given topological ideal triangulation and with prescrib…

Study laws of cosines and sines for hyperbolic shapes with ideal vertices.

Improved bounds on ideal vertices in right-angled hyperbolic polyhedra.

Verifies a conjecture for the figure eight knot.

Ideal attribution mechanisms track model interactions for faithful watermarks.

A dynamical analog of the prime ideals for simple non-commutative rings is introduced. We prove a factorization theorem for the dynamical ideals. The result is used to classify the surface knots and links in the smooth 4-dimensional manifolds.

We provide an example in each rank of an ageometric fully irreducible outer automorphism whose ideal Whitehead graph has a cut vertex. Consequently, we show that there exist examples in each rank of Handel-Mosher axis bundles that are not just a single axis, as well as of "nongeneric" behavior in the sense of the "trai…

We prove that among four-dimensional ideal right-angled hyperbolic polytopes the 24-cell is of minimal volume and of minimal facet number. As a corollary, a dimension bound for ideal right-angled hyperbolic polytopes is obtained.

Paper analyzes $\mathrm{U}(n)$-structures and their minimal left ideals.

Study on knot types using thickness and length constraints.

This short note gives a geometric interpretation of the Atiyah class of a Lie pair. It proves that it vanishes if the subalgebroid is the kernel of a fibration of Lie algebroids. In other words, the Atiyah class of a Lie pair vanishes if the subalgebroid is the fiber of an ideal system in the Lie algebroid. In order to…

Study the Hessian geometry of an ideal gas in a centrifuge.

New method finds ideal circle patterns on spheres.

Study shows how certain knots and tori are detected by ideal points in character varieties.

This article addresses the two significant aspects of Ozsváth and Szabó's knot Floer cube of resolutions that differentiate it from Khovanov and Rozansky's HOMFLY-PT chain complex: (1) the use of twisted coefficients and (2) the appearance of a mysterious non-local ideal. Our goal is to facilitate progress on Rasmussen…

Paper connects geometric structures to algebra in high dimensions.

We extend Nadel's results on some conditions for the multiplier ideal sheaves to satisfy which are described in terms of an obstruction defined by the first author. Applying our extension we can determine the multiplier ideal sheaves on toric del Pezzo surfaces which do not admit Kähler-Einstein metrics. We also show t…

Aitchison and Rubinstein constructed two knot complements that can be decomposed into two regular ideal dodecahedra. This paper shows that these knot complements are the only knot complements that decompose into n regular ideal dodecahedra, providing a partial solution to a conjecture of Neumann and Reid.

The Frohman Kania-Bartoszynska ideal is an invariant associated to a 3-manifold with boundary and a prime p >3. We give some estimates of this ideal. We also calculate this invariant for some 3-manifolds constructed by doing surgery on a knot in the complement of another knot.

Software finds ideal polyhedra with rational dihedral angles and volume maxima.

Minimal biharmonic hypersurfaces in Euclidean spaces are ideal.

The study counts ideal points in 2-bridge knot complements using knot diagrams.

Motivated by deformation quantization, we introduced in an earlier work the notion of formal Morita equivalence in the category of $^*$-algebras over a ring $\ring C$ which is the quadratic extension by $\im$ of an ordered ring $\ring R$. The goal of the present paper is twofold. First, we clarify the relationship betw…