arXiv research

Estimates heights of special surfaces in warped products.

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.

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

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

The paper aims at proving global height estimates for Killing graphs defined over a complete manifold with nonempty boundary. To this end, we first point out how the geometric analysis on a Killing graph is naturally related to a weighted manifold structure, where the weight is defined in terms of the length of the Kil…

In this paper we obtain height estimates for compact, constant mean curvature vertical graphs in the homogeneous spaces $\mathrm{Nil}_3$ and $\widetilde{PSL}_2(\mathbb{R})$. As a straightforward consequence, we announce a structure-type result for proper graphs defined on relatively compact domains.

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.

We construct genomic predictors for heritable and extremely complex human quantitative traits (height, heel bone density, and educational attainment) using modern methods in high dimensional statistics (i.e., machine learning). Replication tests show that these predictors capture, respectively, $\sim$40, 20, and 9 perc…

New method predicts wave height exceedance probabilities.

The paper simplifies arguments for stationary varifolds results.

Signed heights of knotoids are defined and studied.

We will discuss some sharp estimates for CMC graphs in a Riemannian 3-manifold MxR whose boundary is contained in a slice. We will start by giving sharp lower bounds for the geodesic curvature of the boundary and improve these bounds when assuming additional restrictions on the maximum height that such a surface reache…

The aim of this paper is to extend classic results of the theory of CMC surfaces in the product spaces to the class of immersed surfaces in $\mathbb{M}^2(κ)\times\mathbb{R}$ whose mean curvature is given as a $C^1$ function depending on their angle function. We cover topics such as the existence of a priori curvature e…

New height estimate for area minimizing currents, leading to unique tangent cones and decay properties.

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

Constructs currents and heights on K3 surfaces.

In this paper, based on the local comparison principle in [12], we study the local behavior of the difference of two spacelike graphs in a neighborhood of a second contact point. Then we apply it to the constant mean curvature equation in 3-dimensional Lorentz-Minkowski space $\mathbb{L}^3$ and get the uniqueness of cr…

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

The liquid shape between two vertical parallel plates in a gravity field due to capillary forces is studied. When the physical system achieves its mechanical equilibrium, the capillary surface has mean curvature proportional to its height above a horizontal reference plane and it meets the vertical walls in a prescribe…

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

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

We obtain area growth estimates for constant mean curvature graphs in $\mathbb{E}(κ,τ)$-spaces with $κ\leq 0$, by finding sharp upper bounds for the volume of geodesic balls in $\mathbb{E}(κ,τ)$. We focus on complete graphs and graphs with zero boundary values. For instance, we prove that entire graphs in $\mathbb{E}(κ…

In the following text we prove that for all finite $p\geq0$ there exists a topological graph $X$ such that $\{p,p+1,p+2,\ldots\}\cup\{+\infty\}$ is the collection of all possible heights for transformation groups with phase space $X$. Moreover for all topological graph $X$ with $p$ as height of transformation group $(H…

In this paper, we investigate three geometrical invariants of knots, the height, the trunk and the representativity. First, we give a conterexample for the conjecture which states that the height is additive under connected sum of knots. We also define the minimal height of a knot and give a potential example which has…

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 describes singularities of height functions on specific singular surfaces.

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

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,…

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…

In this article, we consider compact surfaces $Σ$ having constant mean curvature $H$ ($H$-surfaces) whose boundary $Γ=\partialΣ\subset \mathbb{M}_0= \mathbb{M} \times_f\{0\}$ is transversal to the slice $\mathbb{M}_0$ of the warped product $\mathbb{M}\times_f\mathbb{R}$, here $\mathbb{M}$ denotes a Hadamard surface…

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…

This paper exhibits equivalences of 2-stacks between certain models of $\mathbb{S}^1$-gerbes and differential 3-cocycles. We focus primarily on the model of Dixmier-Douady bundles, and provide an equivalence between the 2-stack of Dixmier-Douady bundles and the 2-stack of differential 3-cocycles of height 1, where the …

In this paper we consider the evolution of a graph-like hypersurface by anisotropic mean curvature flow, under some restrictions on the anisotropic area integrand. We find interior estimates (in both time and space) on the gradient of such hypersurfaces, depending only on the height of the graph and the anisotropic are…

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

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…

New neural network architecture with height adds expressive power.

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

Differential quantities, including normals, curvatures, principal directions, and associated matrices, play a fundamental role in geometric processing and physics-based modeling. Computing these differential quantities consistently on surface meshes is important and challenging, and some existing methods often produce …

Proves a fundamental gap lower bound for horoconvex domains in hyperbolic space.

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

Minimal submanifolds confined in space are highly restricted.

Smooth solutions found for modified mean curvature flow in Riemannian manifolds.

Given $H\in [0,\infty),$ some sufficient conditions for existence of CMC $H$ graphs with boundary in two parallel planes of $\mathbb{H}^2\times\mathbb{R}$ are presented. Height estimates for outwards-oriented CMC surfaces (horo)cyllindrically bounded are also exhibited.

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