arXiv research

Proves an Euler-type formula for Möbius strip partitions.

Study Euler class of surface bundles with nontrivial results.

This paper classifies semi-equivelar maps on a special surface.

Extending our previous work on eigenvalues of closed surfaces and work of Otal and Rosas, we show that a complete Riemannian surface S of finite type and negative Euler characteristic has at most negative of the Euler characteristics many small eigenvalues.

Unified product Lie groups and their quotient spaces are analyzed for dynamics.

The Euler characteristic is the only additive topological invariant for spaces of certain sort, in particular, for manifolds with some finiteness properties. A generalization of the notion of a manifold is the notion of a V-manifold. Here we discuss a universal additive topological invariant of V-manifolds: the univers…

There are (at least) two different approaches to define equivariant analogue of the Euler charateristic for a space with a finite group action. The first one defines it as an element of the Burnside ring of the group. The second approach emerged from physics and includes the orbifold Euler characteristic and its higher…

Researchers found two types of graphs for 6D torus manifolds with Euler number 6.

Geometric framework for dissipative systems on Lie algebroids.

New equations for Cosserat media motions derived from bundle automorphisms.

If a real value invariant of compact combinatorial manifolds (with or without boundary) depends only on the number of simplices in each dimension on the manifold, then the invariant is completely determined by Euler characteristics of the manifold and its boundary. So essentially, Euler characteristic is the unique inv…

Semi-Equivelar maps are generalizations of Archimedean solids to the surfaces other than 2-sphere. In earlier work a complete classification of semi-equivelar map of type $(3^5, 4)$ on the surface of Euler characteristic -1 was given. In the meantime Karabas an Nedela classified vertex transitive semi-equivelar maps on…

New invariant $c_{sm}$ simplifies computing geometric invariants of recursive group orbits.

Study on the Euler-Plateau energy with elastic modulus, focusing on minimizers and critical surfaces.

This article is concerned with the question: For which pairs of hyperbolic Euler-Lagrange systems in the plane does there exist a rank-$1$ Bäcklund transformation relating them? We express some obstructions to such existence in terms of the local invariants of the Euler-Lagrange systems. In addition, we discover a clas…

The paper derives new Gauss-Bonnet formulas for frontal bundles over surfaces with boundary.

Develops multifactor approximations for SVEs with completely monotone kernels.

Classifies semi-equivelar gems on surfaces with Euler characteristic -1.

Optical interpretation of Euler's angle problem for caustics of light rays.

Study Euler characteristic of manifolds with almost nonnegative curvature operator, showing nonnegativity under certain conditions.

Two types of 4-manifolds disagree on minimum Euler characteristic.

The article explores symmetric maps on surfaces, focusing on semi-equivelar maps.

Study Loday algebroids, prove splitting theorem, and linearize problems.

New bounds on Euler characteristics for certain manifolds with finite groups.

Paper studies rigidity phenomena for elliptic systems on Riemannian manifolds.

We analyze exponential integrability properties of the Cox-Ingersoll-Ross (CIR) process and its Euler discretizations with various types of truncation and reflection at 0. These properties play a key role in establishing the finiteness of moments and the strong convergence of numerical approximations for a class of sto…

Characterizes components of representations space for punctured surfaces.

Non-vanishing steady Euler flows and Beltrami fields found in high dimensions.

Study simulates Heston-type local stochastic volatility model using particle method.

Proves a Gel'fand-Kolmogoroff type result for vector bundles and polynomial functions.

The paper shows how Scherk-type surfaces can be decomposed into helicoids.

The paper proves that certain stationary hypersurfaces in high dimensions are essentially flat.

Constructs homologies for ribbon graphs to recover Penrose polynomials.

In this paper we consider type-preserving representations of the fundamental group of the three--holed projective plane into $\mathrm{PGL}(2, \R) =\mathrm{Isom}(\HH^2)$ and study the connected components with non-maximal euler class. We show that in euler class zero for all such representations there is a one simple cl…

The paper studies Einstein-Hilbert action on complex manifolds.

A classical result says that a free action of the circle $\Bbb{S}^1$ on a topological space $X$ is geometrically classified by the orbit space $B$ and by a cohomological class ${H}^{^{2}}{(B,\Bbb{Z})}$, the Euler class. When the action is not free we have a difficult open question: $Π$ : "Is the space $X$ determined by…

Defines discrete differential geometry concepts in homotopy type theory.

The paper finds a geometric lower bound for the first positive eigenvalue of the rough Laplacian on 1-forms.

We consider the fractional Nirenberg problem on the standard sphere $\mathbb{S}^n$ with $n\geq 4$. Using the theory of critical points at infinity, we establish an Euler-Hopf type formula and obtain some existence results for curvature satisfying assumptions of Bahri-Coron type.

Study classifies 3D Hessian manifolds, proving their topology.

Two methods improve simulation of European call options under Heston model.

We consider a class of stochastic path-dependent volatility models where the stochastic volatility, whose square follows the Cox-Ingersoll-Ross model, is multiplied by a (leverage) function of the spot price, its running maximum, and time. We propose a Monte Carlo simulation scheme which combines a log-Euler scheme for…

The paper derives Gauss-Bonnet formulas for mappings between surfaces with boundary.

Study new Willmore-type variational problem for foliated hypersurfaces.

The purpose of this paper is to show that, at least for Lagrangians of mechanical type, nonholonomic Euler-Lagrange equations for a nonholonomic linear constraint D may be viewed as non-constrained Euler-Lagrange equations but on a new (generally not Lie) algebroid structure on D. The proposed novel formalism allows us…

ENN neural network learns logical syllogisms using Euler diagrams.

Let T be the nilpotent group of 4 x 4 real upper triangular matrices. In this note we show that the Euler equations of certain left-invariant riemannian metrics on T have a horseshoe. We also show, with the aid of a numerical computation of a Melnikov-type integral, that the Euler equations of the sub-riemannian Carnot…

As for the theory of maximal representations, we introduce the volume of a Zimmer's cocycle $Γ\times X \rightarrow \mbox{PO}^\circ(n, 1)$, where $Γ$ is a torsion-free (non-)uniform lattice in $\mbox{PO}^\circ(n, 1)$, with $n \geq 3$, and $X$ is a suitable standard Borel probability $Γ$-space. Our numerical invariant ex…