arXiv research

Study on minimal hypersurfaces in Schwarzschild manifolds intersecting the horizon orthogonally.

We prove that a large class of smooth solutions $ψ$ to the linear wave equation $\Box_gψ=0$ on subextremal rotating Kerr spacetimes which are regular and decaying along the event horizon become singular at the Cauchy horizon. More precisely, we show that assuming appropriate upper and lower bounds on the energy along t…

Classifies and analyzes the stability of black hole event horizon birth points using contact geometry.

New concepts of barriers and black regions defined for Lorentzian manifolds.

Market dynamic is quantified in terms of the entropy $S(τ,n)$ of the clusters formed by the intersections between the series of the prices $p_t$ and the moving average $\widetilde{p}_{t,n}$. The entropy $S(τ,n)$ is defined according to Shannon as $\sum P(τ,n)\log P(τ,n),$ with $P(τ,n)$ the probability for the cluster t…

The study generalizes curvature bounds for manifolds with boundary.

We study the quasi-local energy (QLE) and the surface geometry for Kerr spacetime in the Boyer-Lindquist coordinates without taking the slow rotation approximation. We also consider in the region $r\leq2m$, which is inside the ergosphere. For a certain region, $r>r_{k}(a)$, the Gaussian curvature of the surface with co…

Proves rigidity of extremal Kerr-Newman horizons.

The paper examines how closed curves on surfaces intersect and how this intersection determines the curves.

3-manifold triangulation can be reconstructed from its intersection matrix.

Develops a formalism for studying general horizons and derives a near-horizon equation.

We consider axisymmetric stationary dirty black holes with regular non-extremal or extremal horizons, and compute their on-horizon Petrov types. The Petrov type (PT) in the frame of the observer crossing the horizon can be different from that formally obtained in the usual (but singular in the horizon limit) frame of a…

The paper finds diffeomorphic complex intersections with distinct Hodge numbers.

New polynomials defined for virtual knots, calculated up to crossing 4.

In this paper we present the algorithms for calculating the differential geometric properties {t,n,b1,b2,b3,k1,k2,k3,k4} along-with geodesic curvature and geodesic torsion of the transversal intersection curve of four hypersurfaces (given by parametric representation) in Euclidean space R^5. In transversal intersection…

New insights into black hole horizons from asymptotic expansions.

We generalize the PL intersection product for chains on PL manifolds and for intersection chains on PL stratified pseudomanifolds to products of locally finite chains on non-compact spaces that are natural with respect to restriction to open sets. This is necessary to sheafify the intersection product, an essential ste…

Conditions for curves on a torus with specific pairwise intersections.

Study self-intersections of arcs on a pair of pants, proving natural number spectrum.

Virtual knots with same writhe polynomial have equivalent intersection graphs.

The study reveals distinct patterns in retail investors' holding periods affecting stock returns.

Study properties of self-similar continua with finite intersection property.

Estimates intersection pairing in hyperbolic 4-manifolds.

Paper studies apparent horizon dynamics and introduces a null comparison principle.

By considering a (not necessarily locally-flat) PL knot as the singular locus of a PL stratified pseudomanifold, we can use intersection homology theory to define intersection Alexander polynomials, a generalization of the classical Alexander polynomial invariants for smooth or PL locally-flat knots. We show that the i…

Classifies arcs on a 4-punctured sphere that intersect at most once.

The article discusses new horizons in black hole physics.

James McClure recently showed that the domain for the intersection pairing of PL chains on a PL manifold $M$ is a subcomplex of $C_*(M)\otimes C_*(M)$ that is quasi-isomorphic to $C_*(M)\otimes C_*(M)$ and, more generally, that the intersection pairing endows $C_*(M)$ with the structure of a partially-defined commutati…

Novel approach for large genus intersection number asymptotics.

The paper calculates self-intersections on a pair of pants using Bowen and Series' coding.

Generic potential primes have no self-intersections or intersections.

Study examines Wang-Yau quasi-local energy in strong fields near apparent horizons.

This paper studies the utility maximization problem with changing time horizons in the incomplete Brownian setting. We first show that the primal value function and the optimal terminal wealth are continuous with respect to the time horizon $T$. Secondly, we exemplify that the expected utility stemming from applying th…

Proves symmetries of extremal horizons in spacetimes.

Proves intrinsic rigidity of extremal horizons, classifying their geometry.

Extreme black holes with $\SU(2)$ symmetry have a specific near horizon geometry.

Paper proves curves can be smoothed to reduce self-intersection by exactly 1.

The paper extends intersection theory for b-divisors, proving monotonicity and volume inequalities.

Study intersection polynomials of long virtual knots with supporting genera.

Paper computes Atiyah class for DG manifolds of amplitude +1.

Minimum algebraic intersection found in hyperbolic surfaces, growing with genus.

We continue here the investigation of the relationship between the intersection of a pair of subgroups of a Kleinian group, and in particular the limit set of that intersection, and the intersection of the limit sets of the subgroups. Of specific interest is the extent to which the intersection of the limit sets being …

This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do…

ElasTST improves time-series forecasting across varying horizons.

In this paper we study relations between intersection numbers on moduli spaces of curves and Hurwitz numbers. First, we prove two formulas expressing Hurwitz numbers of (generalized) polynomials via intersections on moduli spaces of curves. Then we show, how intersection numbers can be expressed via Hurwitz numbers. An…

Proves conditions for Cauchy horizons in low-regularity spacetimes.

This paper presents a novel framework for accurate pedestrian intent prediction at intersections. Given some prior knowledge of the curbside geometry, the presented framework can accurately predict pedestrian trajectories, even in new intersections that it has not been trained on. This is achieved by making use of the …

Study the intersection of positive closed currents using tangent currents and King's residue formula.