arXiv research

Study on convex surfaces in Minkowski space, proving completeness and incompleteness conditions.

Classification and regression tasks in overparameterized models show different generalization properties.

Proves globally hyperbolic spacetimes via null distance completeness.

The paper connects hyperbolic spinors to non-null framed curves in Minkowski 3-space.

Proves limit curve theorem for incomplete metric spaces, applies to null distance in Lorentzian manifolds.

This paper explores the relation between convex functions and the geometry of space-times and semi-Riemannian manifolds (an investigation initiated by Gibbons-Ishibashi). Specifically, we study geodesic connectedness. We give geometric-topological proofs of geodesic connectedness for classes of space-times to which kno…

Global existence and geometry of constant mass aspect function foliation in perturbed Schwarzschild spacetime studied.

We define an explicit quasi-local mass functional which is non-decreasing along all foliations (satisfying a convexity assumption) of null cones. We use this new functional to prove the null Penrose conjecture under fairly generic conditions.

Null-Calibrated Conformal Selection via Target-Membership Scores

Minimal surfaces in Heisenberg group have null curves and lines.

We introduce the notion of $k$-type slant helix in Minkowski space $\e_1^4$. For partially null and pseudo null curves in $\e_1^4$, we express some characterizations in terms of their curvature and torsion functions.

Note: Causality can be encoded without strict time function choice.

We consider the goodness-of-fit testing problem of distinguishing whether the data are drawn from a specified distribution, versus a composite alternative separated from the null in the total variation metric. In the discrete case, we consider goodness-of-fit testing when the null distribution has a possibly growing or…

Constructs surfaces with constant mean curvature in Schwarzschild spacetime near null infinity.

The null distance for Lorentzian manifolds was recently introduced by Sormani and Vega. Under mild assumptions on the time function of the spacetime, the null distance gives rise to an intrinsic, conformally invariant metric that induces the manifold topology. We show when warped products of low regularity and globally…

The null energy condition is characterized via convexity of entropy in Lorentzian manifolds.

Study shows instability of naked singularities in scalar field models.

The main result of this paper is a characterization of the minimal surface hull of a compact set $K$ in $\mathbb R^3$ by sequences of conformal minimal discs whose boundaries converge to $K$ in the measure theoretic sense, and also by $2$-dimensional minimal currents which are limits of Green currents supported by conf…

Null distance encodes causal structure in spacetimes.

New null distance bounds confirm Big Bang singularity in cosmological models.

Synthetic framework for null hypersurfaces in non-smooth spacetimes.

In this note, we define a new invariant of a Legendrian knot in a contact manifold using an open book decomposition supporting the contact structure. We define the support genus sg(L) of a Legendrian knot L in a contact 3-manifold (M, ξ) as the minimal genus of a page of an open book of M supporting the contact structu…

The study examines null curves in specific geometric manifolds and their properties.

The paper proves uniform Temple charts and applies them to null distance metrics.

The paper tackles noisy functional data by exploring a multivariate perspective.

The paper studies convergence of cosmological spacetimes using null distance.

It is shown that locally conformally flat Lorentzian gradient Ricci solitons are locally isometric to a Robertson-Walker warped product, if the gradient of the potential function is non null, and to a plane wave, if the gradient of the potential function is null. The latter gradient Ricci solitons are necessarily stead…

Paper connects surfaces in 4D and 3D spacetime.

Theory for gravity coupled with fields on manifolds with null-boundary.

Estimates bandwidth for CMC initial data sets.

There are two important statements regarding the Trautman-Bondi mass at null infinity: one is the positivity, and the other is the Bondi mass loss formula, which are both global in nature. In this note, we compute the limit of the Wang-Yau quasi-local mass on unit spheres at null infinity of an asymptotically flat spac…

The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a funtional on surfaces and studying its properties along a null hypersurface $Ω$ extending to past null infinity. We prove a general Penrose-type inequality which involves the limit at infinity of the Hawki…

Method predicts rarity of image features to support research integrity investigations.

The paper challenges the smooth null infinity model by constructing counter-examples and showing non-smoothness of null infinity.

There are two important statements regarding the Trautman-Bondi mass [1,8,5] at null infinity: one is the positivity [7,6], and the other is the Bondi mass loss formula [1], which are both global in nature. The positivity of the quasi-local mass can potentially lead to a local description at null infinity. This is conf…

The local structure of half conformally flat gradient Ricci almost solitons is investigated, showing that they are locally conformally flat in a neighborhood of any point where the gradient of the potential function is non-null. In opposition, if the gradient of the potential function is null, then the soliton is a ste…

The main topic of this paper is to show that in the 3-dimensional Minkowski spacetime, the torsion of a null curve is equal to the Schwarzian derivative of a certain function appearing in a description of the curve. As applications, we obtain descriptions of the slant helices, and null curves for which the torsion is o…

The authors study a generalized notion of null geodesic defined by the Legendrian dynamics of a regular conical subbundle of the tangent bundle on a manifold. A natural extension of the Weyl tensor is shown to exist, and to depend only on this conical subbundle. Given a suitable defining function of the conical bundle,…

We calculate the limits of the quasi-local angular momentum and center-of-mass defined by Chen-Wang-Yau \cite{CWY} for a family of spacelike two-spheres approaching future null infinity in an asymptotically flat spacetime admitting a Bondi-Sachs expansion. Our result complements earlier work of Chen-Wang-Yau \cite{CWY2…

Proves existence of solutions with concentrated energy in 2+1 spacetime.

The paper proves smoothness of stationary varifolds.

Deep networks show less disorder and more monotonic behavior.

We consider the optimal control problem for null curves in de Sitter 3-space defined by a functional which is linear in the curvature of the trajectory. We show how techniques based on the method of moving frames and exterior differential systems, coupled with the reduction procedure for systems with a Lie group of sym…

We prove that every function $f:\mathbb{R}^n\to \mathbb{R}$ satisfies that the image of the set of critical points at which the function $f$ has Taylor expansions of order $n-1$ and non-empty subdifferentials of order $n$ is a Lebesgue-null set. As a by-product of our proof, for the proximal subdifferential $\partial_{…

The paper finds pseudo-Anosov-like maps on an infinite ladder surface.

Given a time function $τ$ on a spacetime $M$, we define a `null distance function', $\hat{d}_τ$, built from and closely related to the causal structure of $M$. In basic models with timelike $\nabla τ$, we show that 1) $\hat{d}_τ$ is a definite distance function, which induces the manifold topology, 2) the causal struct…

In this study, we define a family of null curves in Minkowski 3-space and called null similar curves. We obtain some properties of these special curves. We show that two null curves are null similar curves if and only if these curves form a null Bertrand pair. Moreover, we obtain that the family of null geodesics and n…

We study the existence of closed trajectories of a particle model on null curves in anti-de Sitter 3-space defined by a functional which is linear in the curvature of the particle path. Explicit expressions for the trajectories are found and the existence of infinitely many closed trajectories is proved.