Eigenvalues of Dirac operators on boundaries are large mass limits.
problem Eigenvalue calculation of Dirac operators on hypersurfaces.
method Limits of Euclidean Dirac operators with mass terms.
result Eigenvalues of boundary Dirac operators are limits of Euclidean ones.
Study of large mass limits of G2 and Calabi-Yau monopoles on specific manifolds.
problem Understanding the behavior of monopoles in the large mass limit on G2 and Calabi-Yau manifolds.
method Developed a structure theory for the limit of SU(2) G2-monopoles and Calabi-Yau monopoles, extracting singular abelian G2-monopoles with Dirac singularities. result Proved an energy identity for monopole bubbles in the large mass limit.
The paper shows how to create scalar flat metrics with very large ADM mass.
problem Understanding the ADM mass of scalar flat Kähler ALE spaces.
method Blowing up points in ALE spaces to increase ADM mass.
result It is possible to produce scalar flat metrics with arbitrarily large ADM mass.
Mass in relativity linked to polyhedra geometry.
problem Mass in general relativity.
method Riemannian polyhedra geometry.
result Mass connected to polyhedra geometry.
Mass in relativity linked to polyhedra geometry.
problem Understanding ADM mass in general relativity.
method Relating ADM mass to the total mean curvature and defect of dihedral angles of Riemannian polyhedra.
result Expressed n-dimensional mass as an integral of geometric quantities. In this paper we characterize the intrinsic geometry of apparent horizons (outermost marginally outer trapped surfaces) in asymptotically flat spacetimes; that is, the Riemannian metrics on the two sphere which can arise. Furthermore we determine the minimal ADM mass of a spacetime containing such an apparent horizon. …
Upper bounds on Bartnik mass for non-negatively curved spheres.
problem Bounding Bartnik mass for non-negatively curved spheres.
method Establishing upper bounds using non-negative Gauss curvature.
result Upper bounds on Bartnik mass approach Hawking mass under certain conditions.
Study the mass of flat 3-manifolds with boundary using specific methods.
problem Calculate the mass of asymptotically flat 3-manifolds with boundary.
method Use the method of Bray-Kazaras-Khuri-Stern to derive a mass formula.
result Derive sufficient conditions for the positivity of the mass.
New mass definition for negative cosmological constant spacetimes.
problem Defining quasilocal mass for spacetimes with negative cosmological constant.
method Spinorial approach based on previous work for vanishing cosmological constant.
result Non-negative mass, equal to Misner-Sharp mass in spherical symmetry, zero for AdS.
Study mass and center of mass in flat 3-manifolds, proving existence of foliations.
problem Interplay between mass, center of mass, and isoperimetric quotients in asymptotically flat 3-manifolds.
method Adapted implicit function method and foliation techniques.
result Existence of foliations satisfying curvature conditions and unique relative isoperimetric surfaces.
We describe explicitly the large volume isoperimetric regions of a natural class of asymptotically flat manifolds, in any dimension. These isoperimetric regions detect the mass and the center of mass of such manifolds when viewed as initial data sets for the Einstein equations in general relativity. Using the positivit…
In this paper, we will study the limiting behavior of the Brown-York mass of the coordinate spheres in an asymptotically flat manifold. Limiting behaviors of volumes of regions related to coordinate spheres are also obtained, including a discussion on the isoperimetric mass introduced by Huisken \cite{Huisken}. We will…
Refines geometric center of mass analysis for Einstein field equations.
problem Analyzing the geometric center of mass of Willmore surfaces in initial data for Einstein field equations.
method Refined Lyapunov-Schmidt analysis to study geometric center of mass of area-constrained Willmore surfaces.
result The geometric center of mass agrees with the Hamiltonian center of mass under specific conditions.
Study of Dirac-like operators on spin manifolds with large mass parameters.
problem Understanding spectra of Dirac-like operators with piecewise constant mass terms.
method Analysis of asymptotic regimes to derive effective operators.
result Extension of MIT Bag operator concept to spin geometry.
Formula calculates mass using cube faces and edges.
problem Measuring mass of 3-manifolds.
method Cube faces and edges, mean curvature, dihedral angle, geodesic curvature, angle defect.
result Mass formula connects to Gromov's theory and Gauss-Bonnet theorem.
We study the mass at the origin in the uncorrelated SABR stochastic volatility model, and derive several tractable expressions, in particular when time becomes small or large. As an application--in fact the original motivation for this paper--we derive small-strike expansions for the implied volatility when the maturit…
In this paper, we study the relation of the monotonicity of Hawking Mass and geometric flow problems. We show that along the Hamilton-DeTurck flow with bounded curvature coupled with the modified mean curvature flow, the Hawking mass of the hypersphere with a sufficiently large radius in Schwarzschild spaces is monoton…
Study large mass G2 and Calabi--Yau monopoles, proving convergence and identifying key sets.
problem Large mass limits of G2 and Calabi--Yau monopoles on specific manifolds. method Common Θ-monopole framework, variational compactness theory, and finer analysis. result Identifies currents and shows saturation of calibration inequalities; defines sets S, Z, and C. Study of Brown--York mass for four-dimensional asymptotically flat manifolds.
problem Calculating mass for hypersurfaces in four-dimensional asymptotically flat manifolds.
method Intrinsic definition of mean curvature, expansion analysis for large uniformly convex hypersurfaces.
result Shape-dependent correction to ADM mass for nearly round surfaces vanishes under certain conditions.
Study on large mass monopoles focusing on their limiting behavior and properties.
problem Analyzing the limiting behavior of sequences of mSU(2) monopoles with large Yang--Mills--Higgs energies. method Bubbling analysis and finite cardinality bounds on the blow-up set and zero set.
result For large mass monopoles, the zero set and blow-up set coincide and are finite sets of points.
We present a set of global invariants, called "mass integrals", which can be defined for a large class of asymptotically hyperbolic Riemannian manifolds. When the "boundary at infinity" has spherical topology one single invariant is obtained, called the mass; we show positivity thereof. We apply the definition to confo…
The paper proves partial rigidity of Hawking mass for stable CMC spheres in specific manifolds.
problem Rigidity of Hawking mass for stable CMC spheres in asymptotic flat and hyperbolic manifolds.
method Mean-field equation and monotonicity of Hawking mass, combined with Shi's rigidity results.
result If the Hawking mass of a nearly round stable CMC surface vanishes, the surface must be a standard sphere in R^3 and the interior is flat.
Proves mass theorem for manifolds with arbitrary ends.
problem Proving the positive mass theorem for manifolds with various ends.
method Quantitative analysis of scalar curvature on manifolds with arbitrary ends.
result Proves the positive mass theorem for a wide class of manifolds.
Proves the validity of Bartnik's mass minimization conjecture for some specific 3-balls.
problem Bartnik's conjecture on mass minimization for asymptotically flat extensions of 3-balls.
method Analyzes Riemannian 3-balls with non-negative scalar curvature and proves the existence or non-existence of mass-minimizing extensions.
result Validates the second part of Bartnik's conjecture for some specific cases but disproves the first part.
We extend Brill's positive mass theorem to a large class of asymptotically flat, maximal, U(1)2-invariant initial data sets on simply connected four dimensional manifolds Σ. Moreover, we extend the local mass angular momenta inequality result Ref [1] for U(1)2 invariant black holes to the case with nonzero stre…
The study finds constraints on scalar curvature using maps and potential theory.
problem Largeness constraints in scalar curvature geometry.
method Basic splitting results and potential theory on singular area minimizing hypersurfaces.
result Non-existence of positive scalar curvature metrics on enlargeable manifolds.
In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the outcomes that have not been seen in a given sample which is an important quantity…
In this paper, we develop a general study of contributions at infinity of Bochner-Weitzenböck-type formulas on asymptotically flat manifolds, inspired by Witten's proof of the positive mass theorem. As an application, we show that similar proofs can be obtained in a much more general setting as any choice of an irreduc…
We extend Witten's spinor proof of the positive mass theorem to large classes of complete asymptotically flat non-spin manifolds, including all manifolds of dimension less than or equal to 11 and all manifolds of dimension less than 26 which admit a codimension 3 immersion in Euclidean space.
The study examines the behavior of monopoles as their mass increases and finds that they abelianize near singular points.
problem The behavior of monopoles as their mass increases and the formation of singular points.
method Analysis of mass-renormalized energy measures and convergence of fields to a reducible monopole.
result The mass-renormalized energy measures concentrate at singular points, and the fields abelianize near these points.
The paper studies constant harmonic mean curvature surfaces in Schwarzschild spaces, proving they foliate the space.
problem Investigating constant harmonic mean curvature surfaces in Schwarzschild spaces.
method Volume-preserving harmonic mean curvature flow in asymptotically Schwarzschild spaces.
result These surfaces form a foliation of the space outside a large ball.
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 …
We analyse the issue of uniqueness of solutions of the static vacuum Einstein equations with prescribed geometric or Bartnik boundary data. Large classes of examples are constructed where uniqueness fails. We then discuss the implications of this behavior for the Bartnik quasi-local mass. A variational characterization…
The paper proves nonexistence of NNSC cobordism for Bartnik data under certain conditions.
problem Proving nonexistence of NNSC cobordism for Bartnik data (Σ1n−1,γ1,H1) and (Σ2n−1,γ2,H2). method Analyzing metrics γ1 and γ2 on Sn−1 with fixed mean curvature H1 and large enough H2 to prove nonexistence of NNSC cobordism. result Proves nonexistence of NNSC cobordism for Bartnik data under specific conditions.
Improved protein identification in mass spectrometry data.
problem Expanding peptide scoring capabilities in tandem mass spectrometry.
method Deriving concave emission distributions for dynamic Bayesian networks.
result Efficiently learned scoring function outperforms state-of-the-art.
Recent advances in statistical theory, together with advances in the computational power of computers, provide alternative methods to do mass-univariate hypothesis testing in which a large number of univariate tests, can be properly used to compare MEEG data at a large number of time-frequency points and scalp location…
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…
CR Yamabe flow fails to converge on small deformations of the standard CR three-sphere.
problem CR Yamabe flow convergence
method Constructing a contact form with negative pseudohermitian mass
result CR Yamabe flow fails to converge on small deformations of the standard CR three-sphere
Consider a triple of "Bartnik data" (Σ,γ,H), where Σ is a topological 2-sphere with Riemannian metric γ and positive function H. We view Bartnik data as a boundary condition for the problem of finding a compact Riemannian 3-manifold (Ω,g) of nonnegative scalar curvature whose boundary is isometric to (Σ,γ)…
New criteria detect anomaly detection algorithms without labeled data.
problem Lack of labeled data for evaluating anomaly detection algorithms.
method Developed two new criteria based on Excess-Mass and Mass-Volume curves, and a feature sub-sampling methodology.
result Empirically validated new criteria outperform classical ROC and PR curves in non-labeled data scenarios.
Study proves catenoids can't exist in certain flat spaces.
problem Existence of minimal catenoids in asymptotically flat spaces.
method Analyzes 3-manifolds with specific mass and catenoid neck sizes.
result Catenoids cannot be found in these spaces due to mass constraints.
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…
Researchers found unique large stable spheres in specific 3D space.
problem Characterizing large stable spheres in specific types of 3D space.
method Unconditional characterization of spheres using Riemannian geometry.
result Global uniqueness of large stable spheres in asymptotically flat Riemannian three-manifolds.
A censored transformed model for proportional outcomes with boundary mass and an application to loss given default modeling.
problem Modeling proportional outcomes with boundary mass in loss given default (LGD) modeling.
method Zero-one censored transformed normal (ZOC-TN) model.
result Captures a wider range of qualitative density shapes than benchmark models while being parsimonious, computationally efficient, and numerically stable.
Estimates the probability of discovering a new type in samples from a population.
problem Estimating the missing mass of unknown type proportions in samples.
method Bayesian nonparametric tools and Good-Turing estimator for regularly varying type proportions.
result The Good-Turing estimator is rate optimal under regularly varying type proportions.
Extends static vacuum metrics with specific boundary conditions.
problem Proving the existence of static vacuum metrics with prescribed boundary data.
method Introducing static regular types (I) and (II), showing local well-posedness, and confirming Bartnik's conjecture.
result Confirms Bartnik's static vacuum extension conjecture for a broad range of boundary conditions.
Two masses on surfaces with boundary converge to ADM mass.
problem Evaluating quasi-local masses on surfaces with boundaries.
method Hawking mass and Huisken's isoperimetric mass on surfaces with boundary, convergence to ADM mass.
result Convergence of Hawking and Huisken's masses to ADM mass.
SPT predicts age and mass of red giants from spectra.
problem Challenges in age and mass estimation of red giants using traditional methods.
method SPT framework with Multi-head Hadamard Self-Attention and Mahalanobis distance-based loss function.
result Remarkable age and mass estimations with low errors and uncertainties.