arXiv research

The Hawking energy is nonnegative and rigid on area-constrained surfaces in general relativity.

New foliations found for critical surfaces of Hawking energy, resolving discrepancies.

Constructs foliations of critical surfaces for Hawking energy in asymptotically flat initial data sets.

New model uses variance-Hawkes process to fit energy market returns.

Optimal energy trading strategy for intraday markets using Hawkes processes.

We investigate the Hawking energy of small surfaces in space times without symmetry assumptions by introducing the notion of Hawking type functionals. In particular, we find that Hawking type functionals are generalized Willmore functionals which allows us to find area constrained, minimizing, immersed, haunted bubble …

The paper proves a Hawking-type singularity theorem using worldvolume quantum strong energy inequalities.

In this work we obtain the limit of the Hawking energy of a large class of foliations along general null hypersurfaces $Ω$ satisfying a weak notion of asymptotic flatness. The foliations are not required to be either geodesic or approaching large spheres at infinity. The limit is obtained in terms of a reference backgr…

New PDE systems generalize Hawking mass monotonicity.

We discuss the Ricci-flat `model metrics' on $\mathbb{C}^2$ with cone singularities along the conic $\{zw=1\}$ constructed by Donaldson using the Gibbons-Hawking ansatz over wedges in $\mathbb{R}^3$. In particular we describe their asymptotic behavior at infinity and compute their energies.

The Penrose theorem and Hawking's topology theorem are extended to weighted spacetimes.

Study on stability of surfaces in null cones under area-preserving variations.

In this sequel paper we give a shorter, second proof of the monotonicity of the Hawking mass for time flat surfaces under spacelike uniformly area expanding flows in spacetimes that satisfy the dominant energy condition. We also include a third proof which builds on a known formula and describe a class of sufficient co…

Positive energy theorems for spin initial data with charge in higher dimensions.

Investigates how 'green' labels affect bond market dynamics.

We show that the Hawking--Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of $C^{1, 1}$-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for $C^{1,1}$-metrics, an…

We prove a version the Penrose inequality for black hole space-times which are perturbations of the Schwarzschild exterior in a slab around a null hypersurface $\underline{\mathcal{N}}_0$. $\underline{\mathcal{N}}_0$ terminates at past null infinity $\mathcal{I}^-$ and $\mathcal{S}_0:=\partial\underline{\mathcal{N}}_0$…

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

We study the evolution of the renormalized volume functional for asymptotically Poincare-Einstein metrics (M,g) which are evolving by normalized Ricci flow. In particular, we prove that the time derivative of the renormalized volume along the flow is the negative integral of scal(g(t)) + n(n-1) over the manifold. This …

Hawking's theorem on the topology of black holes asserts that cross sections of the event horizon in 4-dimensional asymptotically flat stationary black hole spacetimes obeying the dominant energy condition are topologically 2-spheres. This conclusion extends to outer apparent horizons in spacetimes that are not necessa…

Paper proves Penrose inequality with a weaker late-time condition.

Scalar-tensor gravitation theories, such as the Brans-Dicke family of theories, are commonly partly described by a modified Einstein equation in which the Ricci tensor is replaced by the Bakry-Émery-Ricci tensor of a Lorentzian metric and scalar field. In physics this formulation is sometimes referred to as the "Jordan…

Many classical results in relativity theory concerning spherically symmetric space-times have easy generalizations to warped product space-times, with a two-dimensional Lorentzian base and arbitrary dimensional Riemannian fibers. We first give a systematic presentation of the main geometric constructions, with emphasis…

Unified approach to various energy conditions in spacetime geometry.

Researchers prove a 30-year-old cosmological conjecture about spacetime.

Paper proposes a new method for predicting DER adoption with hierarchical guarantees.

Study on stellar models' topology and mass using minimal surfaces.

Study optimal transport on null hypersurfaces and null energy condition.

We introduce a notion of generalized Willmore functionals motivated by the Hawking energy of General Relativity and bending energies of membranes. An example of a bending energy is discussed in detail. Using results of Y. Chen and J. Li, we present a compactness result for branched, immersed, haunted, stratified surfac…

Proves properties of free boundary stable MOTS in spacetimes.

Methodology for estimating marked Hawkes processes with neural networks.

The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-f…

The problem of quasilocal energy has been extensively studied mainly in four dimensions. Here we report results regarding the quasilocal energy in spacetime dimension $n\geq 4$. After generalising three distinct quasilocal energy definitions to higher dimensions under appropriate assumptions, we evaluate their small sp…

Synthetic framework for null hypersurfaces in non-smooth spacetimes.

The paper establishes curvature inequalities and rigidity results for surfaces in Riemannian and Lorentzian geometry.

Derives a pricing formula for VIX options using a new stochastic volatility model.

The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has immigration-birth representation. Based on that, Fierro et al. recently introduced…

On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein square distance from optimal transportation. These notions also make sense in a (nonsmooth) metric measure setting, where they…

Study applies Hawkes volatility to mid-price process for real-time risk management.

It is well-know that Hawking mass is nonnegative for a stable constant mean curvature ($CMC$) sphere in three manifold of nonnegative scalar curvature. R. Bartnik proposed the rigidity problem of Hawking mass of stable $CMC$ spheres. In this paper, we show partial rigidity results of Hawking mass for stable $CMC$ spher…

New optimal investment strategies for finance and insurance using Hawkes-based models.

The paper develops Hawkes-based models for LOB and applies them to European, spread, and basket option pricing.

Introduces a new Hawkes model with CARMA(p,q) intensity to better model dependence structures.

Paper proposes a neural network for non-parametric Hawkes process kernel estimation.

The study examines Hawkes processes and their long-term behavior.

Mamba Hawkes Process improves modeling of event sequences with long-term dependencies.

Sharp bounds for charged Hawking mass in electrostatic space-times.

Flexible nonlinear Hawkes processes for time-varying systems.