arXiv research

Study proves hyperfiniteness of mapping class group actions on surface graphs.

We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces.

We extend the notion of unicorn paths between two arcs introduced by Hensel, Przytycki and Webb to the case where we replace one arc with a geodesic asymptotic to a lamination. Using these paths, we give new proofs of the results of Klarreich and Schleimer identifying the Gromov boundaries of the curve graph and the ar…

The paper proves conjectures about Minkowski norms with specific symmetry groups.

Finsleroid-Finsler metrics form an important class of singular (y-local) Finslerian metrics. They were introduced by G. S. Asanov in 2006. As a special case Asanov produced examples of Landsberg spaces of dimension at least three that are not of Berwald type. These are called Unicorns [5]. The existence of regular (y -…

New algorithm detects unique events in time series data.

Study shows saddle connection graph's geometry and quasi-isometry properties.

This paper addresses the problem of existence of generalized Landsberg structures on surfaces using the Cartan-Kähler Theorem and a Path Geometry approach.

A gap in the proof of the finsler "unicorn" conjecture in the paper "Regular Landsberg metrics are always Berwald" by Z. I. Szabo is pointed out

Deep learning helps identify promising startups.

A new method to value IPOed companies.

The paper provides an intrinsic proof of a theorem about Landsberg spaces.

Study uses web search data to analyze tech startups growth.

Classifies cosmological Finsler spacetimes, finding viable non-stationary models.

Given a Finsler space, we introduce a system of partial differential equations, called the Landsberg equation. Based on a careful analysis of the Landsberg equation and the observation that the solution space is invariant under the linear isometries of the tangent Minkowski spaces, we prove that an $(α_1, α_2)$-metric …

Characterizes spherical Finsler metrics satisfying a specific condition.

In this paper, we study general $(α,β)$-metrics which $α$ is a Riemannian metric and $β$ is an one-form. We have proven that every weak Landsberg general $(α,β)$-metric is a Berwald metric, where $β$ is a closed and conformal one-form. This show that there exist no generalized unicorn metric in this class of general $(…

Solves a PDE for Landsberg surfaces using new Finsler surface insights.

The paper classifies Landsberg spherically symmetric Finsler metrics in various dimensions.

It is still a long-standing open problem in Finsler geometry, is there any regular Landsberg metric which is not Berwaldian. However, there are non-regular Landsberg metrics which are not Berwladian. The known examples are established by G. S. Asanov and Z. Shen. In this paper, we use the Maple program to study some ex…

Finsleroid-Finsler metrics form an important class of singular (y-local) Finsler metrics. They were introduced by G. S. Asanov [2] in 2006. As the special case of the general construction Asanov produced singular (y - local) examples of Landsberg spaces of dimension at least three that are not of Berwald type. The exis…

Predicting startup success using Crunchbase data and deep learning.

Geodesic sprays on Finsler manifolds studied with covariant coefficients.