arXiv research

Constructs positive energy representations from Toda equations Stokes data.

The study examines representations of compactly supported diffeomorphisms with a positive energy condition.

Survey article on loop groups and their representations, following a course of three lectures held at the summer school "algebraic groups" at the Georg-August-Universitaet zu Goettingen, June 27--July 13, 2005. We discuss loop groups, their central extensions, and positive energy representations.

We construct projective unitary representations of the smooth Deligne cohomology group of a compact oriented Riemannian manifold of dimension 4k+1, generalizing positive energy representations of the loop group of the circle. We also classify such representations under a certain condition. The number of the equivalence…

Motivated by positive energy representations, we classify those continuous central extensions of the compactly supported gauge Lie algebra that are covariant under a 1-parameter group of transformations of the base manifold.

We study the space of Killing fields on the four dimensional AdS spacetime $AdS^{3,1}$. Two subsets $\mathcal{S}$ and $\mathcal{O}$ are identified: $\mathcal{S}$ (the spinor Killing fields) is constructed from imaginary Killing spinors, and $\mathcal{O}$ (the observer Killing fields) consists of all hypersurface orthog…

Abstract reviews hyperbolic positive energy theorems.

Paper extends positive energy theorem to anti-de Sitter spacetimes.

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

Motivated by the important work of Brown adn York on quasilocal energy, we propose definitions of quasilocal energy and momentum surface energy of a spacelike 2-surface with positive intrinsic curvature in a spacetime. We show that the quasilocal energy of the boundary of a compact spacelike hypersurface which satisfie…

We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with index given by positive energy representation of loop group. This generalizes the quantization of Hamiltonian $G$-spaces to quasi-Hamiltonian…

New proof shows spacetime energy is always positive in higher dimensions.

Measuring comodules are defined and shown to provide a useful generalization of the set of maps between modules with a broad range of applications. Three applications are described. Connections on bundles are described in terms of measuring comodules, enabling curvature to be defined under general algebraic circumstanc…

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

Proves positive energy conjecture for a specific metric class.

We establish the positive energy theorem for weak asymptotically anti-de Sitter initial data sets with distributional curvature under the weak dominant energy condition.

We define the total energy-momenta for (4+1)-dimensional asymptotically anti-de Sitter spacetimes, and prove the positive energy theorem for such spacetimes.

The paper proves positive energy-momentum theorems for charged AdS initial data sets.

In this paper, energy function is used to investigate the eigen-solutions of $-Δu+ Vu=λu$ on the Riemannian manifolds. We give a new way to prove the positivity of the initial energy of energy function, which leads to a simple way to obtain the growth of eigen-solutions.

We provide a direct proof for the positivity of Chen-Nester-Tung quasi-local energy with analytic reference in spherical symmetry. A hoop-type theorem for this energy is also established. Finally, the relation between Chen-Nester-Tung and Brown-York quasi-local energies will be discussed.

Proves positive mass theorem for spin initial data sets with arbitrary ends and dominant energy shields.

We give a short review of recent progress on the positive energy theorem in general relativity, especially for spacetimes with nonzero cosmological constant.

We establish a type of positive energy theorem for asymptotically anti-de Sitter Einstein-Maxwell initial data sets by using Witten's spinoral techniques.

Paper proves stability of positive mass theorem for specific types of manifolds.

In LM, we proved a family version of the famous Witten rigidity theorems and several family vanishing theorems for elliptic genera. In this paper, we gerenalize our theorems LM in two directions. First we establish a family rigidity theorem for the Dirac operator on loop space twisted by general positive energy loop gr…

We extend the positive mass theorem proved previously by the author to the Lorentzian setting. This includes the original higher dimensional positive energy theorem whose spinor proof was given by Witten in dimension four and by Xiao Zhang in dimension five.

Strict plurisubharmonicity proven for Teichmüller energy on Hitchin representations.

This study proves energy bounds in specific AdS spacetimes.

New energy definition for expanding de Sitter spacetime with umbilic boundaries.

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

The paper proves energy theorems for specific initial data sets in 3D spacetime.

Minimal energy local systems on curves are compact components of character varieties.

Energy functional on Teichmüller space is plurisubharmonic but not strictly so.

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…

Researchers found a way to measure energy in black hole perturbations.

Elliptic Chern characters and Atiyah-Witten formula generalized to double loop spaces.

New proof shows equality in spacetime mass theorem.

Proves spacetime positive mass theorem with corners.

A generalized positive energy theorem for spaces with asymptotic SUSY compactification involving non-symmetric data is proved. This work is motivated by the work of Dai [D1][D2], Hertog-Horowitz-Maeda [HHM], and Zhang [Z].

The paper extends the spacetime positive mass theorem to multiple time dimensions.

Proves positive mass theorem for hyperbolic manifolds with ends.

We prove positivity of energy for a class of asymptotically locally hyperbolic manifolds in dimensions $4\le n \le 7$. The result is established by first proving deformation-of-mass-aspect theorems in dimensions $n\ge 4$. Our positivity results extend to the case $n = 3$ when more stringent conditions are imposed.

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

Low-precision DNNs have been extensively explored in order to reduce the size of DNN models for edge devices. Recently, the posit numerical format has shown promise for DNN data representation and compute with ultra-low precision in [5..8]-bits. However, previous studies were limited to studying posit for DNN inference…

We prove the following stronger verson of the positivity of quasi-local mass stated in gr-qc/0303019: the quasi-local energy (mass) of each connected component of the boundary of a compact spacelike hypersurface which satisfies the local energy condition is strictly positive unless the spacetime is flat along the space…

CLuP achieves near optimal ground state energies for positive and negative Hopfield models.

The paper proves a reverse isoperimetric inequality and applies it to analyze surface flows.

We study biharmonic maps between Riemannian manifolds with finite energy and finite bi-energy. We show that if the domain is complete and the target of non-positive curvature, then such a map is harmonic. We then give applications to isometric immersions and horizontally conformal submersions.