arXiv research

Solves a problem posed by Brezis and Mironescu about least mass of area-minimizing currents.

New algorithm detects anomalies by forcing samples to displace mass in low-density regions.

For asymptotically hyperbolic manifolds of dimension $n$ with scalar curvature at least equal to $-n(n-1)$ the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic manifolds which are …

By Federer and Fleming there exist at least one mass-minimizing normal current in every real-valued homology class of a Riemannian manifold. However the regularity of the mass-minimizing currents and their distributions may generally be quite complicated. In this paper we shall study how to construct nice metrics so th…

In the asymptotically locally hyperbolic setting it is possible to have metrics with scalar curvature at least -6 and negative mass when the genus of the conformal boundary at infinity is positive. Using inverse mean curvature flow, we prove a Penrose inequality for these negative mass metrics. The motivation comes fro…

Paper proves stronger Penrose inequality with matter density.

Given a Riemannian 3-ball $(\bar B, g)$ of non-negative scalar curvature, Bartnik conjectured that $(\bar B, g)$ admits an asymptotically flat (AF) extension (without horizons) of the least possible ADM mass, and that such a mass-minimizer is an AF solution to the static vacuum Einstein equations, uniquely determined b…

We are concerned with obtaining novel concentration inequalities for the missing mass, i.e. the total probability mass of the outcomes not observed in the sample. We not only derive - for the first time - distribution-free Bernstein-like deviation bounds with sublinear exponents in deviation size for missing mass, but …

The study examines the index of MOTS in Kerr-Newman-de Sitter spacetime and its relation to mass and charge.

The paper solves a partial Plateau problem using $H$-mass.

Positive mass theorem for tori with scalar curvature bounds.

This work originates from a heart's images tracking which is to generate an apparent continuous motion, observable through intensity variation from one starting image to an ending one both supposed segmented. Given two images p0 and p1, we calculate an evolution process p(t, \cdot) which transports p0 to p1 by using th…

We prove the Riemannian Penrose conjecture, an important case of a conjecture made by Roger Penrose in 1973, by defining a new flow of metrics. This flow of metrics stays inside the class of asymptotically flat Riemannian 3-manifolds with nonnegative scalar curvature which contain minimal spheres. In particular, if we …

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…

Quite a number of distinct versions of Bartnik's definition of quasi-local mass appear in the literature, and it is not a priori clear that any of them produce the same value in general. In this paper we make progress on reconciling these definitions. The source of discrepancies is two-fold: the choice of boundary cond…

Proves rigidity of sphere metrics with subsets removed.

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…

Bayesian method for multivariate autoregressive models with exogenous inputs.

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

The paper proves a theorem linking convex body centroids and category theory.

Mammography is the most effective and available tool for breast cancer screening. However, the low positive predictive value of breast biopsy resulting from mammogram interpretation leads to approximately 70% unnecessary biopsies with benign outcomes. Data mining algorithms could be used to help physicians in their dec…

Let $M^n$, $n\ge3$, be a compact differentiable manifold with nonpositive Yamabe invariant $σ(M)$. Suppose $g_0$ is a continuous metric with $V(M, g_0)=1$, smooth outside a compact set $Σ$, and is in $W^{1,p}_{loc}$ for some $p>n$. Suppose the scalar curvature of $g_0$ is at least $σ(M)$ outside $Σ$. We prove that $g_0…

The stability of physical systems depends on the existence of a state of least energy. In gravity, this is guaranteed by the positive energy theorem. For topological reasons this fails for nonsupersymmetric Kaluza-Klein compactifications, which can decay to arbitrarily negative energy. For related reasons, this also fa…

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

Consider a compact Riemannian manifold M of dimension n whose boundary \partial M is totally geodesic and is isometric to the standard sphere S^{n-1}. A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at least n(n-1), then M is isometric to the hemisphere S_+^n equipped with its standard metri…

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

An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with singularities conjugate to ADE-type is proved. In 1988, Claude Lebrun gave examples of scalar-flat Kähler ALE metrics with negative mass, on the total space of the bundle $\mathcal{O}(-n)$ over $S^2$. A corollary of this index …

Equivalence proven for isocapacitary mass notions.

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

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.

Mass in relativity linked to polyhedra geometry.