arXiv research

Fibre surfaces in 3-sphere can have unbounded stabilisation height.

Common positive stabilisation found for isotopic contact structures.

Study stabilizers in handlebody group; meridians are undistorted, others are exponentially distorted.

Study of tree automorphisms via arc-stabilizers.

This paper models and evaluates contagion and stabilisation in interconnected financial markets.

Signed heights of knotoids are defined and studied.

Stabilizes deep Bayesian neural networks with self-stabilizing priors.

New proof of Giroux Correspondence for tight contact 3-manifolds.

Estimates heights of special surfaces in warped products.

Study of height jumps in Ceresa cycle using asymptotic Hodge theory.

Study Swan modules and homotopy types, resolving Wall and Dyer questions.

New distances defined between surfaces in 4-manifolds, with a new inequality proved.

In dimension 3 and above, Bredon cohomology gives an acurate purely algebraic description of the minimal dimension of the classifying space for actions of a group with stabilisers in any given family of subgroups. For some Coxeter groups and the family of virtually cyclic subgroups we show that the Bredon cohomological…

The study finds all possible heights for transformation groups on graphs.

Constructs currents and heights on K3 surfaces.

Genomic predictors explain 40% of human height variance.

Paper proves unbounded stabilization heights of fiber surfaces using Hopf invariant.

The paper explores knots' height, trunk, and representativity, finding gaps and bounds.

Computes canonical heights for arithmetic log surfaces using Hurwitz zeta function.

The abstract discusses connections between K-stability, heights, and rational points on Fano varieties.

Faltings heights help in Kahler geometry stability.

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

We study the singularities of the members of the family of height functions on Whitney umbrellas, which is also known as cross-caps, and show that the family of the height functions is a versal unfolding. Moreover, we study local intersections of a Whitney umbrella with a hyperplane through its singular point.

Defines height pairing for differential forms on Riemann surface degenerations.

Study uses satellite and lidar data to map forest height and biomass in France.

Study describes singularities of height functions on specific singular surfaces.

The paper modifies a warped product space to find conditions for constant height functions.

New method stabilizes GAN training by solving ODEs.

The heights of Alexandroff square transformation groups are computed and proven.

Study stable equivalence relations on 4-manifolds, proving homotopy equivalent manifolds with abelian fundamental group are stably diffeomorphic.

We introduce a new method for detection of long-range cross-correlations and multifractality - multifractal height cross-correlation analysis (MF-HXA) - based on scaling of qth order covariances. MF-HXA is a bivariate generalization of the height-height correlation analysis of Barabasi & Vicsek [Barabasi, A.L., Vicsek,…

The paper proves height estimates for Killing graphs on manifolds.

Persistent Legendrian contact homology distinguishes knots using height functional.

We describe spaces of essential finite height (measured) laminations in a surface $S$ using a parameter space we call $\mathbb S$, an ordered semi-ring. We show that for every finite height essential lamination $L$ in $S$, there is an action of $π_1(S)$ on an $\mathbb S$-tree dual to the lift of $L$ to the universal co…

The paper establishes a relation between knotoid crossing number and height.

The paper connects special cycle heights to Siegel Eisenstein series.

We extend the Faltings modular heights of abelian varieties to general arithmetic varieties and show direct relations with the Kahler-Einstein geometry, the Minimal Model Program, heights of Bost and Zhang, and give some applications. Along the way, we propose arithmetic Yau-Tian-Donaldson conjecture, an equivalence of…

New neural network architecture with height adds expressive power.

We classify, in terms of topology of highest arcs, low height non-simple geodesics on the modular hyperbolic punctured sphere with three elliptic fixed points of order two. Of eight possible types, exactly one consists of geodesics that form a bigon about the cusp; we express all such geodesics in terms of Markoff trip…

We consider height functions on symmetric spaces $M\cong G/K$ embedded in the associated matrix Lie group $G$. In particular we study the relationship between the critical sets of the height function on $G$ and its restriction to $M$. Also we prove that the gradient flow on $M$ can be integrated by means of a generaliz…

It is one of the most important facts in 4-dimensional topology that not every spherical homology class of a 4-manifold can be represented by an embedded sphere. In 1978, M. Freedman and R. Kirby showed that in the simply connected case, many of the obstructions to constructing such a sphere vanish if one modifies the …

The height function of various surfaces decomposes into finite sums of scaled and translated versions of itself.

The study examines the realizability of a 4-manifold invariant for homeomorphisms.

The author constructs height functions and studies their first derivatives on closed manifolds.

Study stabilizes components of Galois cover moduli spaces.

Paper shows equivalences between Dixmier-Douady bundles and differential 3-cocycles.

Sharp bounds on K-semistable Fano varieties for low dimensions.

The paper extends CMC surface theory to product spaces, proving height estimates and classifying surfaces.