arXiv research

We give some lower estimates of the ADM mass of an asymptotically flat (AF) Riemannian manifold without assuming that the scalar curvature of the manifold is nonnegative. Some sufficient conditions for an AF manifold to have nonnegative ADM mass are obtained. We also give some lower estimates of the Brown-York mass of …

Given a constant mean curvature surface that bounds a compact manifold with nonnegative scalar curvature, we obtain intrinsic conditions on the surface that guarantee the positivity of its Hawking mass. We also obtain estimates of the Bartnik mass of such surfaces, without assumptions on the integral of the squared mea…

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

Constructs initial data for Einstein equations and estimates Bartnik mass outside time-symmetry.

Estimates mass of static vacuum metrics with small Bartnik data.

Estimates Bartnik mass for metrics with nonnegative Gauss curvature.

Study on residual Monge-Ampère mass of complex functions with directional Lipschitz continuity.

Given $n$ samples from a population of individuals belonging to different types with unknown proportions, how do we estimate the probability of discovering a new type at the $(n+1)$-th draw? This is a classical problem in statistics, commonly referred to as the missing mass estimation problem. Recent results by Ohannes…

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

Given a sphere with Bartnik data close to that of a round sphere in Euclidean 3-space, we compute its Bartnik-Bray outer mass to first order in the data's deviation from the standard sphere. The Hawking mass gives a well-known lower bound, and an upper bound is obtained by estimating the mass of a static vacuum extensi…

Mantoulidis and Schoen developed a novel technique to handcraft asymptotically flat extensions of Riemannian manifolds $(Σ\cong \mathbb{S}^2,g)$, with $g$ satisfying $λ_1 = λ_1(-Δ_g + K(g))>0$, where $λ_1$ is the first eigenvalue of the operator $-Δ_g+K(g)$ and $K(g)$ is the Gaussian curvature of $g$, with control on t…

New method improves missing mass concentration bounds.

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

The mass of asymptotically hyperbolic ends and manifolds is analyzed.

The Positive Mass Theorem implies that any smooth, complete, asymptotically flat 3-manifold with non-negative scalar curvature which has zero total mass is isometric to (R^3, delta_{ij}). In this paper, we quantify this statement using spinors and prove that if a complete, asymptotically flat manifold with non-negative…

The paper proves a quantitative positive mass theorem for spin manifolds with distance estimates.

Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.

SPT predicts age and mass of red giants from spectra.

We derive a positive mass theorem for asymptotically flat manifolds with boundary whose mean curvature satisfies a sharp estimate involving the conformal Green's function. The theorem also holds if the conformal Green's function is replaced by the standard Green's function for the Laplacian operator. As an application,…

In the context of the Bartnik mass, there are two fundamentally different notions of an extension of some compact Riemannian manifold $(Ω,γ)$ with boundary. In one case, the extension is taken to be a manifold without boundary in which $(Ω,γ)$ embeds isometrically, and in the other case the extension is taken to be a m…

Estimates the mass gap for domains with integral Ricci curvature bounds.

In this article we prove a family of local (in time) weighted Strichartz estimates with derivative losses for the Klein-Gordon equation on asymptotically de Sitter spaces and provide a heuristic argument for the non-existence of a global dispersive estimate on these spaces. The weights in the estimates depend on the ma…

Estimates missing data points in classifier inputs based on training data.

Paper proves mass theorems for nonnegative scalar curvature metrics.

This study calculates the maximum error of a famous estimation method.

Study geometric inequalities and boundary estimates for Einstein-type manifolds with boundary.

Obesity is an important concern in public health, and Body Mass Index is one of the useful (and proliferant) measures. We use Convolutional Neural Networks to determine Body Mass Index from photographs in a study with 161 participants. Low data, a common problem in medicine, is addressed by reducing the information in …

The Bartnik mass is a quasi-local mass tailored to asymptotically flat Riemannian manifolds with non-negative scalar curvature. From the perspective of general relativity, these model time-symmetric domains obeying the dominant energy condition without a cosmological constant. There is a natural analogue of the Bartnik…

We consider an asymptotically flat Riemannian spin manifold of positive scalar curvature. An inequality is derived which bounds the Riemann tensor in terms of the total mass and quantifies in which sense curvature must become small when the total mass tends to zero.

New neural network enforces mass conservation for better ice flow predictions.

In this article, we estimate the quasi-local energy with reference to the Minkowski spacetime [16,17], the anti-de Sitter spacetime [4], or the Schwarzschild spacetime [3]. In each case, the reference spacetime admits a conformal Killing-Yano 2-form which facilitates the application of the Minkowski formula in [15] to …

Paper proves rigidity of 3-manifolds with boundary using modified Hawking mass.

We study the stability of the Positive Mass Theorem using the Intrinsic Flat Distance. In particular we consider the class of complete asymptotically flat rotationally symmetric Riemannian manifolds with nonnegative scalar curvature and no interior closed minimal surfaces whose boundaries are either outermost minimal h…

We define barycentric coordinates on a Riemannian manifold using Karcher's center of mass technique applied to point masses for n+1 sufficiently close points, determining an n-dimensional Riemannian simplex defined as a "Karcher simplex." Specifically, a set of weights is mapped to the Riemannian center of mass for the…

Study on quasi-Einstein manifolds with boundary estimates and inequalities.

Study characterizes compact Einstein-type manifolds with boundary.

In this article, we investigate the connection between scalar curvature and first eigenfunctions via positive mass theorem for Brown-York mass. For compact manifolds with nice boundary, we show that a sharp inequality holds for first eigenfunctions when posing appropriate assumptions on scalar curvature and first eigen…

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

We provide estimates on the Bartnik mass of constant mean curvature (CMC) surfaces which are diffeomorphic to spheres and have positive mean curvature. We prove that the Bartnik mass is bounded from above by the Hawking mass and a new notion we call the asphericity mass. The asphericity mass is defined by applying Hami…

Away from the central axis, we prove the stability of the Positive Mass Theorem in the $W^{1,p}$ sense for asymptotically flat axisymmetric manifolds with nonnegative scalar curvature satisfying some additional technical assumptions. We also derive estimates for the volumes of regions, the areas of axisymmetric surface…

Investigates convexity of minimizers under mass constraint using nonlocal perimeter and potential.

A framework to quantify deployment risk in ML systems, especially for rare states.

Prove Riemannian positive mass theorem for asymptotically flat metrics with low-codimension singularities.

This paper constructs charged Riemannian manifolds to test Penrose inequality.

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

Sharp stability in Almgren problem solved in any dimension.

Derives new monotone quantities for p-harmonic functions on asymptotically flat 3-manifolds.

We present an iterative technique for finding zeroes of vector fields on Riemannian manifolds. As a special case we obtain a ``nonlinear averaging algorithm'' that computes the centroid of a mass distribution supported in a set of small enough diameter D in a Riemannian manifold M. We estimate the convergence rate of o…