arXiv research

Algorithm recovers permutations of high-dimensional Gaussian vectors with constant correlation.

Algorithm matches vertices of correlated Erdős-Rényi graphs efficiently.

Efficient algorithm for graph matching in correlated stochastic block models.

New algorithm achieves almost exact graph matching in almost quadratic time.

We study the hyperbolic random geometric graph introduced in Krioukov et al. For a sequence $R_n \to \infty$, we define these graphs to have the vertex set as Poisson points distributed uniformly in balls $B(0,R_n) \subset B_d^α$, the $d$-dimensional Poincaré ball (unit d-ball with the Poincaré metric $d_α$ correspondi…

Polynomial-time algorithm matches correlated random graphs with non-vanishing correlation.

Alexander polynomial equals spanning tree count at t=1.

A new test statistic counts tree co-occurrences to detect edge correlation between networks.

Paper proves computational hardness for graph matching and detection problems.

The paper develops a stationary-distribution theory for Random Forest ensemble size selection.

The paper explores statistical limits for detecting correlation in tree structures.

Optimal survival trees ensemble reduces tree count and improves predictive performance.

Improved DP KDE with better privacy and efficiency.

Fermat constants fail to fully identify Clairaut constants for certain geodesics on a surface of revolution.

Study proves surfaces with constant curvature are simple shapes.

The paper classifies hypersurfaces in $\mathbb{H}^2 imes\mathbb{H}^2$ with constant curvature.

Study on biconservative hypersurfaces with constant scalar curvature in space forms.

We prove several facts about the Yamabe constant of Riemannian metrics on general noncompact manifolds and about S. Kim's closely related "Yamabe constant at infinity". In particular we show that the Yamabe constant depends continuously on the Riemannian metric with respect to the fine C^2-topology, and that the Yamabe…

Study CR Yamabe constant and CR structures on manifolds.

The paper studies curves of constant-ratio in pseudo-Galilean space.

The Cheeger constant increases under Ricci flow on spheres.

We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant complex angle with respect to a fixed spacelike plane. This notion is the natural Lo…

The paper defines new constants for $p$-Laplacian on manifolds.

Study classifies 3D self-shrinkers with constant second form norm.

In 1926 S. Nakajima (= A. Matsumura) showed that any convex body in $\R^3$ with constant width, constant brightness, and boundary of class $C^2$ is a ball. We show that the regularity assumption on the boundary is unnecessary, so that balls are the only convex bodies of constant width and brightness.

Study refines Siegel-Veech constants for abelian differentials.

Curves with constant torsion can be deformed arbitrarily.

New upper bound for Cheeger constant of hyperbolic surfaces.

Simplified proof for Cheeger's isoperimetric constant.

Study on isoparametric and constant-curvature hypersurfaces in Finsler spaces.

This paper mixes constant sum and constant product market makers to improve their features.

Ruled surfaces with Ricci metrics use curves of constant torsion.

Paper proves a Liouville theorem for solitons with constant curvature.

Estimates eigenvalues and spectrum for graph substructures using isocapacitary constants.

The paper classifies and constructs rotational surfaces with constant astigmatism in space forms.

A number of results for C$^2$-smooth surfaces of constant width in Euclidean 3-space ${\mathbb{E}}^3$ are obtained. In particular, an integral inequality for constant width surfaces is established. This is used to prove that the ratio of volume to cubed width of a constant width surface is reduced by shrinking it along…

Study on surfaces in Heisenberg group with constant mean curvature.

Defines structure constants for specific geometric structures on Lie groups.

Salkowski \cite{salkow}, one century ago, introduced a family of curves with constant curvature but non-constant torsion (Salkowski curves) and a family of curves with constant torsion but non-constant curvature (anti-Salkowski curves) in Euclidean 3-space $\e^3$. In this paper, we adapt definition of such curves to ti…

Study constructs closed curves with constant curvature on cylinders and tori.

It is proved that if an AK2-manifold of dimension greater or equal to 6 is of pointwise constant antiholomorphic sectional curvature, then it is a 6-dimensional manifold of constant negative sectional curvature or a Kähler manifold of constant holomorphic sectional curvature.

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

The study classifies quasi-Einstein manifolds with constant scalar curvature.

Study constant mean curvature surfaces with integrable boundary conditions.

Concrete example of 2-sphere with constant curvature 1 and closed geodesics.

Classifies hypersurfaces with constant curvature in product spaces.

We study the problem of deforming a Riemannian metric to a conformal one with nonzero constant scalar curvature and nonzero constant boundary mean curvature on a compact manifold of dimension $n\geq 3$. We prove the existence of such conformal metrics in the cases of $n=6,7$ or the manifold is spin and some other remai…

Constructs Kähler metrics with constant scalar curvature on blown-up manifolds.