arXiv research

Sharp bounds on Fano varieties' heights proven for specific cases.

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

Minimal submanifolds confined in space are highly restricted.

A comparison-based algorithm finds nearest neighbors in metric spaces.

Signed heights of knotoids are defined and studied.

Estimates heights of special surfaces in warped products.

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

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

The paper classifies affine minimal translation surfaces and finds their properties.

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.

The stabilisation height of a fibre surface in the 3-sphere is the minimal number of Hopf plumbing operations needed to attain a stable fibre surface from the initial surface. We show that families of fibre surfaces related by iterated Stallings twists have unbounded stabilisation height.

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.

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

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…

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

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

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

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

In this paper, we give a height estimate for constant mean curvature graphs. Using this result we prove two results of uniqueness for the Dirichlet problem associated to the constant mean curvature equation on unbounded domains.

New method predicts wave height exceedance probabilities.

DeepMIDE forecasts wind speeds across space, time, and height for offshore wind energy.

The paper derives height estimates for surfaces with constant curvature in warped product spaces.

Given a finite graph of relatively hyperbolic groups with its fundamental group relatively hyperbolic and edge groups quasi-isometrically embedded and relatively quasiconvex in vertex groups, we prove that vertex groups are relatively quasiconvex if and only if all the vertex groups have finite relative height in the f…

The paper simplifies arguments for stationary varifolds results.

The paper estimates heights of H-surfaces in warped products with conditions.

Study enhances neural network predictions for wave height using topological features.

In this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher order mean curvature, and whose boundary is contained into a slice. We apply these results to draw topological conclusions at the end of the paper.

In this paper we prove local results for solutions to the Ricci flow (heat flow) whose speed (height) is bounded by $\frac c t$ for some time interval $t \in (0,T)$. These results are contained in chapter 7 of the author's habilitation thesis, University of Freiburg, Germany, 2006.