Related papers: Initial data set rigidity results for polyhedra
The Witten spinorial argument has been adapted in several works over the years to prove positivity of mass in the asymptotically AdS and asymptotically hyperbolic settings in arbitrary dimensions. In this paper we prove a scalar curvature…
Consider an asymptotically Euclidean initial data set with a smooth marginally trapped surface (possibly a union of future and past multi-connected components) as inner boundary. By a further development of the spinorial framework…
An important, if relatively less well known aspect of the singularity theorems in Lorentzian Geometry is to understand how their conclusions fare upon weakening or suppression of one or more of their hypotheses. Then, theorems with modified…
We develop a theory of Finite Element Systems, for the purpose of discretizing sections of vector bundles, in particular those arizing in the theory of elasticity. In the presence of curvature we prove a discrete Bianchi identity. In the…
We give a survey of various rigidity results involving scalar curvature. Many of these results are inspired by the positive mass theorem in general relativity. In particular, we discuss the recent solution of Min-Oo's Conjecture for the…
Let $(\tilde{\Sigma},h_{ab},K_{ab})$ be an initial data set and let $x^a$ be a symmetry vector of $\tilde{\Sigma}$. Consider a MOTS $\mathcal{S}$ in $\tilde{\Sigma}$ and let the symmetry vector be decomposable along the unit normal to…
We show how rigidity emerges in experiments of sheared frictional granular materials by using generalizations of two methods for identifying rigid structures. Both approaches, the force-based dynamical matrix and the topology-based rigidity…
We characterize spin initial data sets that saturate the BPS bound in the asymptotically AdS setting. This includes both gravitational waves and rotating black holes in higher dimensions, and we establish a sharp dimension threshold in each…
We prove a rigidity theorem in Poisson geometry around compact Poisson submanifolds, using the Nash-Moser fast convergence method. In the case of one-point submanifolds (fixed points), this immediately implies a stronger version of Conn's…
The mechanical response of cellular materials with spinodal topologies is numerically and experimentally investigated. Spinodal microstructures are generated by the numerical solution of the Cahn-Hilliard equation. Two different topologies…
Magnetic dipole-dipole interaction dominated Bose-Einstein condensates are discussed under spinful situations. We treat the spin degrees of freedom as a classical spin vector, approaching from large spin limit to obtain an effective minimal…
The paper deals with the inverse problem of determining a polyhedral inclusion compactly contained in an elastic body from boundary measurements of traction and displacement taken on an open portion of the boundary. Both the inclusion and…
It is well-known that considerations of symmetry lead to the definition of a host of conserved quantities (energy, linear momentum, center of mass, etc.) for an asymptotically flat initial data set, and a great deal of progress in…
The goal of this paper is to investigate the rigidity of 4-dimensional manifolds involving some pinching curvature conditions. To this end, we make use of the approach of biorthogonal curvature which is weaker than the sectional curvature.…
The primary aim of this thesis is to investigate metrics which are induced by a differential form and arise as a critical point of Hitchin's variational principle. Firstly, we investigate metrics associated with the structure group PSU(3)…
The aim of this paper is to extend some basic results about marginally outer trapped surfaces to the context of surfaces having general null expansion. Motivated in part by recent work of Chai-Wan, we introduce the notion of…
This paper considers the coupled problem of a three-dimensional elastic body and a two-dimensional plate, which are rigidly connected at their interface. The plate consists of a plane elasticity model along the longitudinal direction and a…
In this note we study the topology of 3-dimensional initial data sets with horizons of a sort associated with asymptotically locally anti-de Sitter spacetimes. We show that, within this class, those initial data sets which contain no…
In this paper we prove several quantitative rigidity results for conformal immersions of surfaces in $\mathbb{R}^n$ with bounded total curvature. We show that (branched) conformal immersions which are close in energy to either a round…
We formulate and prove a periodic analog of Maxwell's theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove deformation and rigidity-theoretic…