相关论文: Poincare-Einstein Holography for Forms via Conform…
The Poincare function is a compact form of counting moduli in local geometric problems. We discuss its property in relation to V.Arnold's conjecture, and derive this conjecture in the case when the pseudogroup acts algebraically and…
The generalized harmonic representation of Einstein's equation is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
In this article we propose a new geometrization of the radiative phase space of asymptotically flat space-times: we show that the geometry induced on null-infinity by the presence of gravitational waves can be understood to be a…
We present a survey on multiplicity results for the Allen--Cahn equation and systems in the singular perturbation regime, emphasizing their geometric interpretation through $\Gamma$-convergence and isoperimetric theory. In the scalar case,…
We study the holography of the new conformal higher spin theories imposing general boundary conditions and the near horizon boundary conditions. General boundary conditions lead to the asymptotic symmetry algebra which is a loop algebra of…
We introduce partial secondary invariants associated to complete Riemannian metrics which have uniformly positive scalar curvature outside a prescribed subset on a spin manifold. These can be used to distinguish such Riemannian metrics up…
The features of correlated Michelson interferometers are for describing the analysis of Einsteinian spacetime models, and the quantum geometries pertinent with descriptions of GR compatible with particle Physics. Such apparati allow for the…
Solving Einstein's constraint equations for the construction of black hole initial data requires handling the black hole singularity. Typically, this is done either with the excision method, in which the black hole interior is excised from…
We consider the classic problem of a compact fluid source that behaves non-relativistically and that radiates gravitational waves. The problem consists of determining the metric close to the source as well as far away from it. The…
Beginning with the self-dual two-forms approach to the Einstein equations, we show how, by choosing basis spinors which are proportional to solutions of the Dirac equation, we may rewrite the vacuum Einstein equations in terms of a set of…
There has been substantial calculational progress in the last few years for gauge theory amplitudes which involve massless four dimensional particles. One of the central ingredients in this has been the ability to keep precise track of the…
In recent years, gravitational models motivated by quantum corrections to gravity which introduce higher order terms like $R^{2}$ or terms in which the Riemann tensor is not symmetric have been studied by several authors in the form of a…
This paper offers a number of examples showing that in the case of two independent variables the uniform ellipticity of a linear system of differential equations with partial derivatives of the second order, which fulfills condition (3), do…
We present a differential geometric formulation of the Poincare problem using the calculus of moving surfaces (CMS). In this framework, an n dimensional compact hypersurface evolves under a velocity field that couples motion to the…
This paper contributes to the solution of the Poincare problem, which is to bound the degree of a (generalized algebraic) leaf of a (singular algebraic) foliation of the complex projective plane. The first theorem gives a new sort of bound,…
We consider generalized $\alpha$-attractor models whose scalar potentials are globally well-behaved and whose scalar manifolds are elementary hyperbolic surfaces. Beyond the Poincar\'e disk $\mathbb{D}$, such surfaces include the hyperbolic…
The relation between two branches of solutions (radiative and subradiative) of wave equations on Minkowski spacetime is investigated, for any integer spin, in flat Bondi coordinates where remarkable simplifications occur and allow for exact…
The simplices and the complexes arsing form the grading of the fundamental (desymmetrized) domain of arithmetical groups and non-arithmetical groups, as well as their extended (symmetrized) ones are described also for oriented manifolds in…
The conformal-to-Einstein operator is a conformally invariant linear overdetermined differential operator whose non-vanishing solutions correspond to Einstein metrics within a conformal class. We construct compatibility complexes for this…