Related papers: Initial data gluing in the asymptotically flat reg…

Data-driven constitutive modeling is an emerging field in computational solid mechanics with the prospect of significantly relieving the computational costs of hierarchical computational methods. Traditionally, these surrogates have been…

In this article, we revisit the initial data rigidity theorem of Eichmair, Galloway and Mendes (arxiv:2009.09527). The goal is to strengthen their result by showing that the initial data sets concerned carry a vector field that is lightlike…

We study the relationship between asymptotic characteristic initial data at past null infinity and the regularity of solutions at future null infinity for the massless linear spin-s field equations on Minkowski space. By quantitatively…

We prove an asymptotic stability result for a linear coupled hyperbolic-elliptic system on a large class of singular background spacetimes in CMC gauge on the n-torus. At each spatial point these background spacetimes are perturbations of…

We construct transformations which take asymptotically AdS hyperbolic initial data into asymptotically flat initial data, and which preserve relevant physical quantities. This is used to derive geometric inequalities in the asymptotically…

We propose a novel analysis framework for non-descent-type optimization methodologies in nonconvex scenarios based on the Kurdyka-Lojasiewicz property. Our framework allows covering a broad class of algorithms, including those commonly…

For some typical and widely used non-convex half-quadratic regularization models and the Ambrosio-Tortorelli approximate Mumford-Shah model, based on the Kurdyka-\L ojasiewicz analysis and the recent nonconvex proximal algorithms, we…

An interesting question is to characterize the general class of allowed boundary conditions for gauge theories, including gravity, at spatial and null infinity. This has played a role in discussions of soft charges, where antipodal symmetry…

We examine the two-dimensional Euler equations including the local energy (in)equality as a differential inclusion and show that the associated relaxation essentially reduces to the known relaxation for the Euler equations considered…

It is well known that via the augmented Lagrangian method, one can solve Stokes' system by solving the nearly incompressible linear elasticity equation. In this paper, we show that the converse holds, and approximate the inverse of the…

In this article we consider the conformal decomposition of the Einstein constraint equations introduced by Lichnerowicz, Choquet-Bruhat, and York, on asymptotically flat (AF) manifolds. Using the non-CMC fixed-point framework developed in…

This paper investigates asymptotic fixed point results for nonlinear contractions, with emphasis on Kirk-type theorems and their generalizations. A central difficulty in the literature has been the requirement that the mapping possesses a…

Flatness of sampled data systems can be characterized by a simple property. They must admit the transformation to special representations, which are the series or partial series connection of a Brunovsky normal form and a complement. It is…

We prove in a mathematically rigorous way the asymptotic formula of Flaherty and Keller on the effective property of densely packed periodic elastic composites with hard inclusions. The proof is based on the primal-dual variational…

In generalized linear regression problems with an abundant number of features, lasso-type regularization which imposes an $\ell^1$-constraint on the regression coefficients has become a widely established technique. Deficiencies of the…

Nonnegative (linear) least square problems are a fundamental class of problems that is well-studied in statistical learning and for which solvers have been implemented in many of the standard programming languages used within the machine…

We consider the most general asymptotically flat boundary conditions in three-dimensional Einstein gravity in the sense that we allow for the maximal number of independent free functions in the metric, leading to six towers of boundary…

The Spi framework provides a 4-dimensional approach to investigate the asymptotic properties of gravitational fields as one recedes from isolated systems in any space-like direction, without reference to a Cauchy surface. It is well suited…

We prove that "first singularities" in the non-trapped region of the maximal development of spherically symmetric asymptotically flat data for the Einstein-Vlasov system must necessarily emanate from the center. The notion of "first"…

We begin by emphasizing that we are dealing with standard Einstein or Einstein-Maxwell theory - absolutely no new physics has been inserted. The fresh item is that the well-known asymptotically flat solutions of the Einstein-Maxwell theory…