arXiv research

We propose a new approach to the value distribution theory of entire holomorphic curves. We define a ``packing density'' of an entire holomorphic curve, and show that it has various non-trivial properties. We prove a ``gap theorem'' for holomorphic maps from elliptic curves to the complex projective space, and study th…

Curves in higher dimensions are either affine or have super-Euclidean energy growth.

Study shows Calabi-Yau manifolds are non-hyperbolic via mirror symmetry.

Complex projective manifolds without rational curves are quotients of Abelian varieties.

This work evaluates deep generative models using RD curves, providing a more comprehensive quality assessment.

We present two initial graphs over the entire $\mathbb{R}^n$, $n \geq 2$ for which the mean curvature flow behaves differently from the heat flow. In the first example, the two flows stabilize at different heights. With our second example, the mean curvature flow oscillates indefinitely while the heat flow stabilizes. …

We obtain a Bernstein type result for entire two dimensional minimal graphs in $\mathbb{R}^{4}$, which extends a previous one due to L. Ni. Moreover, we provide a characterization for complex analytic curves.

Elliptic curve governs Hopf linking in symmetric tensegrity.

Study finds solitons on curved spaces with varying behavior.

3D filament plots visualize curves in datasets, avoiding visual clutter.

Stable solutions found for a specific physics model.

Proposes a resampling method to compare uplift models with uncertainty.

Constructs the moduli stack of elliptic curves as an orbifold.

We consider portfolio optimization in futures markets. We model the entire futures price curve at once as a solution of a stochastic partial differential equation. The agents objective is to maximize her utility from the final wealth when investing in futures contracts. We study a class of futures price curve models wh…

Unified four trade-off curves for assessing generative model proximity.

The paper shows that energy futures yield curves have an affine geometry.

The study finds solitons for curve shortening flow on hyperbolic plane.

In this paper, we show that any compact K$ä$hler manifold homotopic to a compact Riemannian manifold with negative sectional curvature admits a K$ä$hler-Einstein metric of general type. Moreover, we prove that, on a compact symplectic manifold $X$ homotopic to a compact Riemannian manifold with negative sectional curva…

We develop a new method to construct explicit, regular minimal surfaces in Euclidean space that are defined on the entire complex plane with controlled geometry. More precisely we show that for a large class of planar curves $(x(t), y(t))$ one can find a third coordinate $z(t)$ and normal fields $n(t)$ along the space …

The envelope of straight lines affine normal to a plane curve C is its affine evolute; the envelope of the affine lines tangent to C is the original curve, together with the entire affine tangent line at each inflexion of C. In this paper, we consider plane curves without inflexions. We use some techniques of singulari…

Minimal graphs grow slowly on curved spaces, proving constant solutions.

The geometric torsion conjecture asserts that the torsion part of the Mordell--Weil group of a family of abelian varieties over a complex quasiprojective curve is uniformly bounded in terms of the genus of the curve. We prove the conjecture for abelian varieties with real multiplication, uniformly in the field of multi…

The presence of slipknots in configurations of proteins and DNA has been shown to affect their functionality, or alter it entirely. Historically, polymers are modeled as polygonal chains in space. As an alternative to space curves, we provide a framework for working with subknots inside of knot diagrams via knotoid dia…

The paper proves a rescaling principle for quasiregular curves and applies it to hyperbolicity.

Enhances linear regression with Kalman filter for loss minimization.

Criteria for extending degree-2 Azumaya algebras with C2-actions over curves.

Once first answers in any dimension to the Green-Griffiths and Kobayashi conjectures for generic algebraic hypersurfaces $\mathbb{X}^{n-1} \subset \mathbb{P}^n(\mathbb{C})$ have been reached, the principal goal is to decrease (to improve) the degree bounds, knowing that the `celestial' horizon lies near $d \geqslant 2n…

In the third part of this series we introduce consistent relative value measures for CDS-Bond basis trades using the bond-implied CDS term structure derived from fitted survival rate curves. We explain why this measure is better than the traditionally used Z-spread or Libor OAS and offer simplified hedging and trading …

Study of hyperbolic behavior in complex manifolds with specific vector bundles.

Develops a duality for graphs in Riemannian and Lorentzian spaces with prescribed mean curvature.

A new model for forward curves captures behavior through a single equation.

Study efficient geodesics in curve complex using dot graphs.

The paper studies steady motions of fibre-reinforced fluids on curved surfaces.

Researchers create a projective space for quasimaps and study its connections to Calabi-Yau fibrations.

Study reveals weak knotting in confined polymers, not dominated by any single knot type.

In this paper it is shown that the space of tight geodesic segments connecting any two vertices in a complex of cycles has finite, uniformly bounded dimension. The dimension is defined in terms of a discrete analogue of Jacobi fields, which are explicitly constructed and shown to give a complete description of the enti…

We study classical solutions to the one-phase free boundary problem in which the free boundary consists of smooth curves and the components of the positive phase are simply-connected. We show that if two components of the free boundary are close, then the solution locally resembles an entire solution discovered by Haus…

Knot Floer homology is reinterpreted as immersed curves.

Paper introduces ILD algorithm to determine Bayes error for binary classification.

The study proves inequalities on curved spaces without global curvature bounds.

Unified and extended precision-recall metrics for generative models.

We consider finite-sheeted, regular, possibly branched covering spaces of compact surfaces with boundary and the associated liftable and symmetric mapping class groups. In particular, we classify when either of these subgroups coincides with the entire mapping class group of the surface. As a consequence, we construct …

Study of weakly Kähler hyperbolic manifolds, proving Lang and Green-Griffiths conjectures.

We reformulate Heegaard Floer homology in terms of holomorphic curves in the cylindrical manifold Sigma x [0,1] x R, where Sigma is the Heegaard surface, instead of Sym^g(Sigma). We then show that the entire invariance proof can be carried out in our setting. In the process, we derive a new formula for the index of the…

Zero entropy found in entire Grauert tubes of certain manifolds.

Identifying patients who will be discharged within 24 hours can improve hospital resource management and quality of care. We studied this problem using eight years of Electronic Health Records (EHR) data from Stanford Hospital. We fit models to predict 24 hour discharge across the entire inpatient population. The best …

Develops a method to construct entire minimal graphs of odd dimensions.

Study proves certain Zoll manifolds with entire Grauert tubes are isometric.