arXiv research

New formula shows how causal vectors relate to mass-minimizing data.

In this paper we present upper bounds on the minimal mass of a non-trivial stationary 1-cycle. The results that we obtain are valid for all closed Riemannian manifolds. The first result is that the minimal mass of a stationary 1-cycle on a closed n-dimensional Riemannian manifold M^n is bounded from above by (n+2)!d/3,…

New insights into Bartnik mass from improvability of dominant energy scalar.

Estimates missing mass in Markovian sequences with linear runtime and near-optimal risk.

In [LW], we construct examples of two-dimensional Hamiltonian stationary self-shrinkers and self-expanders for Lagrangian mean curvature flows, which are asymptotic to the union of two Schoen-Wolfson cones. These self-shrinkers and self-expanders can be glued together to yield solutions of the Brakke flow - a weak form…

Estimates stationary mass and frequency from non-i.i.d. data.

It is conjectured that the full (spacetime) Bartnik mass of a surface $Σ$ is realised as the ADM mass of some stationary asymptotically flat manifold with boundary data prescribed by $Σ$. Assuming this holds true for a 1-parameter family of surfaces $Σ_t$ evolving in an initial data set {with the dominant energy condit…

Unified framework for photon and massive particle hypersurfaces in stationary spacetimes.

We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data represent non-stationary, axially symmetric, black holes. As a consequence…

GT estimator shows convergence for Markov samples, improving i.i.d. results.

We prove that every stationary polyhedral varifold minimizes area in the following senses: (1) its area cannot be decreased by a one-to-one Lipschitz ambient deformation that coincides with the identity outside of a compact set, and (2) it is the varifold associated to a mass-minimizing flat chain with coefficients in …

The paper proves a rigidity theorem for null geodesic travel times in asymptotically AdS spacetimes.

Establishes inequality for multiple black holes, proving mass lower bound.

The Riemannian hemisphere has a lower bound for its mass.

I propose a frequency domain adaptation of the Expectation Maximization (EM) algorithm to group a family of time series in classes of similar dynamic structure. It does this by viewing the magnitude of the discrete Fourier transform (DFT) of each signal (or power spectrum) as a probability density/mass function (pdf/pm…

Proves a higher-order positive energy theorem for stationary solutions in fourth-order gravity.

In this paper, based on an intrinsic definition of asymptotically AdS space-times, we show that the standard anti-de Sitter space-time is the unique strictly stationary asymptotically AdS solution to the vacuum Einstein equations with negative cosmological constant in dimension less than 7. Instead of using the positiv…

We study the asymptotic behavior of solutions to the second boundary value problem for a parabolic PDE of Monge-Ampère type arising from optimal mass transport. Our main result is an exponential rate of convergence for solutions of this evolution equation to the stationary solution of the optimal transport problem. We …

We construct one-parameter families of solutions to the Einstein--Klein--Gordon equations bifurcating off the Kerr solution such that the underlying family of spacetimes are each an asymptotically flat, stationary, axisymmetric, black hole spacetime, and such that the corresponding scalar fields are non-zero and time-p…

We solve Bartnik's stationary extension problem near Schwarzschild spheres.

Using the formalism of Lyapunov potential function it is shown that the stability principles for biomass in the ecosystem and for employment in economics are mathematically similar. The ecosystem is found to have a stable and an unstable stationary state with high (forest) and low (grasslands) biomass, respectively. In…

We uniquely and explicitly reconstruct the instantaneous intrinsic metric of the Kerr-Newman Event Horizon from the spectrum of its Laplacian. In the process we find that the angular momentum parameter, radius, area; and in the uncharged case, mass, can be written in terms of these eigenvalues. In the uncharged case th…

New method bypasses global fit for LISA's Galactic binaries, extracting population parameters directly.

New insights into $p$-widths of surfaces, proving optimality and calculating constants.

The X-ADM mass is shown to be equivalent to the ADM mass, proving the X-positive mass theorem in all dimensions.

Graphs with bounded anisotropic mean curvature are regular almost everywhere.

The paper studies nonlinear mass concepts in 3-manifolds with nonnegative scalar curvature.

Equivalence proven for isocapacitary mass notions.

The paper defines a new mass quantity for 3-manifolds and proves a positive mass theorem.

We report on results concerning a partially aggregated Stock Flow Consistent (SFC) macroeconomic model in the stationary state where the sectors of banks and firms are aggregated, the sector of households is dis-aggregated, and the probability density function (pdf) of the wealth of households is exogenous, constrained…

Introduce new boundary mass for asymptotically flat half-manifolds

We prove directly without using a density theorem that (i) the ADM mass defined in the usual way on an asymptotically flat manifold is equal to the mass defined intrinsically using Ricci tensor; (ii) the Hamiltonian formulation of center of mass and the center of mass defined intrinsically using Ricci tensor are the sa…

Continuous metrics on R^3 with specific properties have non-negative harmonic mass.

The paper examines mass aspects at future null infinity and limits of quasilocal mass.

Study the mass of flat 3-manifolds with boundary using specific methods.

Unified definition of mass aspect function for weakly regular hyperbolic manifolds.

Local mass perspective on Bayesian inference

On asymptotically flat and asymptotically hyperbolic manifolds, by evaluating the total mass via the Ricci tensor, we show that the limits of certain Brown-York type and Hawking type quasi-local mass integrals equal the total mass of the manifold in all dimensions.

Simple proof for sphere mass calculation.

New ADM mass definition for weakly regular manifolds.

New theorem for spacetime mass in noncompact regions.

Huisken's isoperimetric mass is always nonnegative.

Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.

New optimal transport method handles mass creation and destruction.

Study on residual Monge-Ampère mass for symmetric plurisubharmonic functions.

Surveying mass in 2D hyperbolic geometry, overcoming challenges via minimisation.

New mass definition linked to ADM mass for general metrics.

The paper connects mass, harmonic functions, and capacity in asymptotically flat 3-manifolds.