A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper analyzes -structures and their minimal left ideals.
Paper connects geometric structures to algebra in high dimensions.
Proves left-orderability of mapping class groups of infinite-type surfaces.
A representation of generalized Weierstrass formulae for an immersion of generic surfaces into a 4-dimensional complex space in terms of spinors treated as minimal left ideals of Clifford algebras is proposed. The relation between integrable deformations of surfaces via mVN-hierarchy and integrable deformations of spin…
Spinor representations of surfaces immersed into 4-dimensional pseudo-riemannian manifolds are defined in terms of minimal left ideals and tensor decompositions of Clifford algebras. The classification of spinor fields and Dirac operators on the immersed surfaces is given. The Dirac-Hestenes spinor field on surfaces im…
The study examines the normalized volumes of right-angled hyperbolic polyhedra and their spectra.
The study proves poor ideal three-edge triangulations are minimal for certain 3-manifolds.
We show that a left invariant metric on a compact Lie group which is obtained by stretching a biinvariant metric in the direction of a subalgebra $\h$ of $\g$ always has some negative sectional curvature, unless the semi-simple part of $\h$ is an ideal of $\g$.
Thurston introduced shear deformations (cataclysms) on geodesic laminations - deformations including left and right displacements along geodesics. For hyperbolic surfaces with cusps, we consider shear deformations on disjoint unions of ideal geodesics. The length of a balanced weighted sum of ideal geodesics is defined…
Previous work of the authors studies minimal triangulations of closed 3-manifolds using a characterisation of low degree edges, embedded layered solid torus subcomplexes and 1-dimensional -cohomology. The underlying blueprint is now used in the study of minimal ideal triangulations. As an application, it …
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.
Minimal biharmonic hypersurfaces in Euclidean spaces are ideal.
Study on Lie groups with exact G2 structures and closed eigenforms.
The study of flat symplectic Lie algebras and groups.
Proves left-orderability of certain Dehn fillings on 3-manifolds.
We study metric contraction properties for metric spaces associated with left-invariant sub-Riemannian metrics on Carnot groups. We show that ideal sub-Riemannian structures on Carnot groups satisfy such properties and give a lower bound of possible curvature exponents in terms of the datas.
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…
Paper finds infinite family of minimal triangulations for complex 3D shapes.
Study shows universal circle isomorphic to flow space ideal boundary.
Every biharmonic Wintgen ideal submanifold in a Riemannian manifold of constant sectional curvature is either minimal or has constant mean curvature.
We develop an invariant of knots that depends on a complex parameter t, describing a left ideal in the noncommutative torus. When the parameter is set equal to -1 we recover the A-polynomial of the knot. We relate the invariant to the colored Jones polynomials of the knot.
Laurent Hauswirth and Harold Rosenberg developed the theory of minimal surfaces with finite total curvature in $\H^2\times\R$. They showed that the total curvature of one such a surface must be a non-negative integer multiple of . The first examples appearing in this context are vertical geodesic planes and Scherk…
The paper proves foliations of solutions to the minimal surface equation in exterior domains.
Study finds knots with ideal length need not have smallest volume.
Maps Lagrangian submanifolds to quaternionic projective space, proving one-to-one correspondences.
Study submanifolds in hyperbolic space, focusing on their boundary and Laplace operator.
New theorem finds new minimal hypersurfaces in hyperbolic space.
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 -ideal and -ideal biharmonic hypersurfaces in Euclidean space …
Starting with an ideal triangulation of the interior of a compact 3-manifold M with boundary, no component of which is a 2-sphere, we provide a construction, called an inflation of the ideal triangulation, to obtain a strongly related triangulations of M itself. Besides a step-by-step algorithm for such a construction,…
Built the smallest non-commensurable hyperbolic 4-manifold.
We study optimal double helices with straight axes (or the fattest tubes around them) computationally using three kinds of functionals; ideal ones using ropelength, best volume packing ones, and energy minimizers using two one-parameter families of interaction energies between two strands of types and $\frac1r…
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…
Generalizing the Cauchy-Riemann equations, we construct the Osserman system of the first order for a pair of two -valued functions on the domain . The graph $\left\{\, \left(x, y, f(x, y), g(x,y) \right) \in {\mathbb{R}}^{4} \, \vert \, (x,y) \in …
The paper proves properties of specific hypersurfaces in a 5-sphere.
A submanifold in a real space form attaining equality in the DDVV inequality at every point is called a Wintgen ideal submanifold. They are invariant objects under the Moebius transformations. In this paper, we classify those Wintgen ideal submanifolds of dimension m>3 which are Moebius homogeneous. There are three cla…
Minimal conformal foliations on Lie groups are shown to be fibres of harmonic morphisms.
Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is an isometric immersion which produces the least possible amount of tension from the ambient space at each point of the submanifold. The main purpose of this paper is to completely classify all non-minimal ideal submanifolds of real …
Minimal vector fields on oscillator groups studied, with specific conditions for minimality.
Study on Lie groups' conformal foliations and harmonic morphisms.
In this paper, we study Lorentzian left invariant Einstein metrics on nilpotent Lie groups. We show that if the center of such Lie groups is degenerate then they are Ricci-flat and their Lie algebras can be obtained by the double extension process from an abelian Euclidean Lie algebra. We show that all nilpotent Lie gr…
The note confirms a conjecture for specific Lie groups.
We define the ideal simplicial volume for compact manifolds with boundary. Roughly speaking, the ideal simplicial volume of a manifold measures the minimal size of possibly ideal triangulations of "with real coefficients", thus providing a variation of the ordinary simplicial volume defined by Gromov in 1982, t…
Study on special Lie groups with Lorentzian metrics.
Various semigroups of noninvertible supermatrices of the special (antitriangle) shape having nilpotent Berezinian which appear in supersymmetric theories are defined and investigated. A subset of them continuously represents left and right zero semigroups and rectangular bands. The ideal properties of higher order rect…
A submanifold in space forms satisfies the well-known DDVV inequality due to De Smet, Dillen, Verstraelen and Vrancken. The submanifold attaining equality in the DDVV inequality at every point is called Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal submanifolds are studied in this paper using…
The paper proves geodesics and conic sections are length-minimizing under specific metrics.
The paper proves conditions for the Abundance conjecture in minimal projective klt pairs.
We study incompressible surfaces constructed by Culler-Shalen theory in the context of twisted Alexander polynomials. For a st cohomology class of a -manifold the coefficients of twisted Alexander polynomials induce regular functions on the -character variety. We prove that if an ideal point giv…