arXiv research

New graph-based method for compact n-manifolds.

Constructs real algebraic functions with both compact and non-compact preimages.

The paper estimates heights of constant mean curvature graphs in specific spaces.

We consider the $Q_k$ flow on complete non-compact graphs. We prove that a complete graph evolves by the $Q_k$ curvature up to some time $T$ depending on the radius of a sphere enclosed by the initial graph.

We study the evolution of convex complete non-compact graphs by positive powers of Gauss curvature. We show that if the initial complete graph has a local uniform convexity, then the graph evolves by any positive power of Gauss curvature for all time. In particular, the initial graph is not necessarily differentiable.

Graphs approximate Laplacian spectra on manifolds.

Defined a new graph type for compact surfaces, proving its connectedness and infinite diameter.

Automates graph convolutional network design for semi-supervised node classification.

A compact 4-dimensional manifold is a non-singular graph-manifold if it can be obtained by the glueing T^2-bundles over compact surfaces (with boundary) of negative Euler characteristics. If none of glueing diffeomorphisms respect the bundle structures, the graph-structure is called reduced. We prove that any homotopy …

Proposes methods for local clustering in attributed graphs.

Every graph can be represented as a singular set of a special surface.

Smooth manifolds can be triangulated with graphs of bounded twin-width.

Let M be a graph manifold. We show that π_1M is the fundamental group of a compact nonpositively curved cube complex if and only if M is chargeless. We also prove that in that case π_1M is virtually compact special.

Study of mapping class groups on infinite graphs, focusing on their large-scale geometry.

The paper extends graph complexity calculations for certain 3-manifolds up to 14.

We introduce a representation of compact 3-manifolds without spherical boundary components via (regular) 4-colored graphs, which turns out to be very convenient for computer aided study and tabulation. Our construction is a direct generalization of the one given in the eighties by S. Lins for closed 3-manifolds, which …

Groups of homotopy equivalences of graphs help realize compact subgroups.

Compact clustering in latent space improves semi-supervised learning.

In this paper, we address the following question: What does a typical compact Riemann surface of large genus look like geometrically? We do so by constructing compact Riemann surfaces from oriented 3-regular graphs. The set for such Riemann surfaces is dense in the space of all compact Riemann surfaces, namely Belyi su…

The study provides a structure theorem for a new class of noncompact 3-manifolds.

The Shannon theorem is extended to locally compact groups.

Minimal graphs over non-compact domains in 3-manifolds solved with estimates and uniqueness results.

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…

Disc graphs are uniformly quasiconvex in curve graphs of surfaces.

Study shows consistency of shallow GCNNs on sampled point clouds under manifold assumption.

In this paper, we show that a nontrivial compact graph manifold is nonpositively curved if and only if its fundamental group virtually embeds into a right-angled Artin group. As a consequence, nonpositively curved graph manifolds have linear fundamental groups.

Non-relatively hyperbolic separating curve graph for surfaces.

This paper is concerned with lower bounds for the connectivity of graphs (one-dimensional skeleta) of triangulations of compact manifolds. We introduce a structural invariant b_M for simplicial d-manifolds M taking values in the range 0 <= b_M <= d-1. The main result is that b_M influences connectivity in the following…

The paper proves removable singularity for nonlocal minimal graphs.

We prove that the existence of a positively defined, invariant Einstein metric $m$ on a connected homogeneous space $G/H$ of a compact Lie group $G$ is the consequence of non-contractibility of some compact set $C=X_{G,H}^Σ$ (Böhm polyhedron) introduced by C.Böhm. There is a natural continuous map of $C$ onto the flag …

Proposes a deep learning approach for attributed graph clustering.

Polynomial algorithm estimates mGH distance between unweighted graphs.

Study geodesic flow on graph-related nilmanifolds, finding integrable and non-integrable cases.

Generalizes Kauffman's clock theorem to surfaces.

Let S be a compact surface, and M be the double of a handlebody. Given a homotopy class of maps from S to M inducing an isomorphism of fundamental groups, we describe a canonical uniformly lipschitz retraction of the sphere graph of M to the arc graph of S. We also show that this retraction is a uniformly bounded dista…

GOTabPFN improves tabular model performance with compact tokenization for HDLSS data.

GLAD learns a compact model to recover sparse graphs from data.

Researchers describe the Gromov boundary of a graph related to surfaces.

We establish existence and uniqueness of compact graphs of constant mean curvature in MxR over bounded multiply connected domains of Mx{0} with boundary lying in two parallel horizontal slices of MxR

The paper studies the connectedness of a graph's boundary for surfaces.

New trick builds hyperbolic manifolds from compact ones, proving some don't virtually fiber.

The paper extends spectral results to non-abelian groups acting on compact Riemannian manifolds.

We prove the connectedness and calculate the diameter of the oriented graph of graftings associated to exotic complex projective structures on a compact surface S with a given holonomy representation of Fuchsian type. The oriented graph of graftings is the graph whose vertices are the equivalence classes of marked CP^1…

Study GKM actions on special manifolds with interval orbit spaces.

In this paper we extend to non-compact Riemannian manifolds with boundary the use of two important tools in the geometric analysis of compact spaces, namely, the weak maximum principle for subharmonic functions and the integration by parts. The first one is a new form of the classical Ahlfors maximum principle whereas …

Laplacian Eigenvectors of the graph constructed from a data set are used in many spectral manifold learning algorithms such as diffusion maps and spectral clustering. Given a graph constructed from a random sample of a $d$-dimensional compact submanifold $M$ in $\mathbb{R}^D$, we establish the spectral convergence rate…

Graph Laplace operators uniquely identify metrics and densities on manifolds.

Diagrammatic method characterizes non-split surfaces in 3-sphere.