arXiv research

Connected domination numbers found for plane triangulations up to 13 vertices.

Constructs covariant derivatives for Ehresmann connections.

Unique vertical isomorphisms between Fedosov dg manifolds are proven for Lie pairs.

We uncover some connections between the topology of a complete Riemannian surface M and the minimum number of vertices, i.e., critical points of geodesic curvature, of closed curves in M. In particular we show that the space forms with finite fundamental group are the only surfaces in which every simple closed curve ha…

In this paper we study some problems related to a vertical Liouville distribution (called vertical Liouville-Hamilton distribution) on the cotangent bundle of a Cartan space. We study the existence of some linear connections of Vrănceanu type on Cartan spaces related to some foliated structures. Also, we identify a cer…

On the slit tangent manifold $TM^0$ of a Finsler space $(M,F)$ there are given some natural foliations as vertical foliation and some other fundamental foliations produced by the vertical and horizontal Liouville vector fields, see [A. Bejancu, H. R. Farran, Finsler Geometry and Natural Foliations on the Tangent Bundle…

Constructs Lepage equivalents for arbitrary-order Lagrangians.

New spectral conditions ensure graph rigidity and global rigidity in the Euclidean plane.

We study the existence and uniqueness problem of compact minimal vertical graphs in $\mathbb{H}^n\times\mathbb{R}$, $n\geq 2$, over bounded domains in the slice $\mathbb{H}^n\times\{0\}$, with non-connected boundary having a finite number of $C^0$ hypersufaces homeomorphic to the sphere $\mathbb{S}^{n-1}$, with prescri…

Classifies 3-manifolds from simplified (2,0)-trisections of 4-manifolds.

Rectangular diagrams of links are link diagrams in the plane ${\mathbb R}^2$ such that they are composed of vertical line segments and horizontal line segments and vertical segments go over horizontal segments at all crossings. P. R. Cromwell and I. A. Dynnikov showed that rectangular diagrams of links are useful for d…

We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a Schwarz-Christoffel formula for periodic polygons in the plane. Our surfaces share the property that vertical symmetry planes cut them into simply connected pieces.

We present the census of all non-orientable, closed, connected 3-manifolds admitting a rigid crystallization with at most 30 vertices. In order to obtain the above result, we generate, manipulate and compare, by suitable computer procedures, all rigid non-bipartite crystallizations up to 30 vertices.

Study of Poincaré-Reeb graphs for algebraic domains.

Connected graph for twice-punctured torus curves.

An unknotting tunnel in a 3-manifold with boundary is a properly embedded arc, the complement of an open neighborhood of which is a handlebody. A geodesic with endpoints on the cusp boundary of a hyperbolic 3-manifold and perpendicular to the cusp boundary is called a vertical geodesic. Given a vertical geodesic in a h…

An embedding of a graph into $\mathbb{R}^3$ is said to be linear, if any edge of the graph is sent to be a line segment. And we say that an embedding $f$ of a graph $G$ into $\mathbb{R}^3$ is free, if $π_1(\mathbb{R}^3-f(G))$ is a free group. It was known that for any complete graph its linear embedding is always free.…

Generalized Lagrange-Weyl structures and compatible connections are introduced as a natural generalization of similar notions from Riemannian geometry. Exactly as in Riemannian case, the compatible connection is unique if certain symmetry conditions with respect to vertical and horizontal Christoffel symbols are impose…

Establishes equivalent formulations of connections in tangent categories.

Paper classifies surface-links using charts with specific properties.

New proof shows extendable shellability for simple complexes.

The paper solves the Integration Problem for principal connections.

A new asynchronous method for vertical federated learning improves privacy and efficiency.

The paper examines vertical curves and fibers in the Heisenberg group, proving properties and constructing counterexamples.

New graphs show hierarchical hyperbolic properties, extending previous work.

Various curve complexes with vertices representing multicurves on a surface $S$ have been defined, for example [3], [4] and [8]. The homology curve complex $\mathcal{HC}(S,α)$ defined in [7] is one such complex, with vertices corresponding to multicurves in a nontrivial integral homology class $α$. Given two multicurve…

We prove that any non-simply connected planar domain can be properly and minimally embedded in H^2 x R. The examples that we produce are vertical bi-graphs, and they are obtained from the conjugate surface of a Jenkins-Serrin graph.

New algorithm finds corrupted vertices in graphs with few queries.

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. In…

New bounds on triangulations of manifolds with non-free fundamental groups.

We prove that the universal covering of a complete locally symmetric normal metric contact pair manifold is a Calabi-Eckmann manifold. Moreover we show that a complete, simply connected, normal metric contact pair manifold such that the foliation induced by the vertical subbundle is regular and reflections in the integ…

Efficiently searches ancestral graphs using multivariate information.

Optimal coupling among random vectors with known statistics and correlation structure found using minimum spanning tree over measure-valued vertices.

Moves connect multibranched surfaces with same neighborhoods.

A new algorithm reduces graph complexity for better dense subgraph analysis.

Automorphisms of fine 1-curve graph linked to surface homeomorphisms.

We compare two ways of interpreting higher order connections. The geometric approach lies in the decomposition of higher order tangent space into the horizontal and vertical structures while the jet--like approach considers a higher order connection as the section of a jet prolongation of a fibered manifold. Particular…

Estimates graph connected components from sampled subgraphs.

Graphs with given k vertices generate an (acyclic) simplicial complex. We describe the homology of its quotient complex, formed by all connected graphs, and demonstrate its applications to the topology of braid groups, knot theory, combinatorics, and singularity theory. The multidimensional analogues of this complex ar…

The main purposes of this article are to extend our previous results on homogeneous sprays to arbitrary (generalized) sprays, to show that locally diffeomorphic exponential maps can be defined for any (generalized) spray, and to give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. I…

The study constructs minimal hypersurfaces in $M imes\mathbb{R}$ with helicoid and catenoid properties.

This paper tackles exact recovery of clusters in a stochastic Ising model on a SBM graph.

Spheres in curve graphs are connected, proving Gromov boundary linearity.

Study of sub-Riemannian problem on specific Lie groups, revealing symmetries and bounds.

The paper defines vector 1-forms on Finsler manifolds and constructs connections.

For an arrangement of $n$ pseudolines in the real projective plane let us denote by $t_i$ the number of vertices incident to $i$ lines. We obtain a linear on $t_i$ inequality similar to the Hirzebruch one, but with an elementary proof. We present an algorithm for producing lower bounds of the number of regions basing o…

A new discrete formula connects vertex and edge distributions on graphs.

A special spine of a three-manifold is said to be poor if it does not contain proper simple subpolyhedra. Using the Turaev-Viro invariants, we establish that every compact three-dimensional manifold M with connected nonempty boundary has a finite number of poor special spines. Moreover, all poor special spines of the m…