Related papers: Stability of the Positive Mass Theorem for Axisymm…

We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to $\#^{g}(S^{n+1}\times S^{n})$, provided $n \geq 4$. This is an odd dimensional analogue of a recent homological stability result of S. Galatius and…

We prove a stability theorem for families of holomorphically-parallelizable manifolds in the category of Hermitian manifolds.

We study the stability of the Positive Mass Theorem (PMT) and the Riemannian Penrose Inequality (RPI) in the case where a region of an asymptotically flat manifold $M^3$ can be foliated by a smooth solution of Inverse Mean Curvature Flow…

Inspired by asymptotically flat manifolds, we introduce the concept of asymptotically flat graphs and define the discrete ADM mass on them. We formulate the discrete positive mass conjecture based on the scalar curvature in the sense of…

We prove Conjecture F from [VW12] which states that the complements of closures of certain strata of the symmetric power of a smooth irreducible complex variety exhibit rational homological stability. Moreover, we generalize this conjecture…

We prove that homological stability holds for configuration spaces of orbifolds. This builds on the work of Bailes' thesis where he proves that the stabilisation maps are injective.

A well-known property of unordered configuration spaces of points (in an open, connected manifold) is that their homology stabilises as the number of points increases. We generalise this result to moduli spaces of submanifolds of higher…

We define an ADM-like mass, called p-mass, for an asymptotically flat pseudohermitian manifold. The p-mass for the blow-up of a compact pseudohermitian manifold (with no boundary) is identified with the first nontrivial coefficient in the…

We prove the stability in weighted $W^{1,1}$ spaces for standard finite element approximations of the Poisson equation in convex polygonal or polyhedral domains, when the weight belongs to Muckenhoupt's class $A_1$ and the family of meshes…

This paper concerns piecewise-smooth maps on $\mathbb{R}^d$ that are continuous but not differentiable on switching manifolds (where the functional form of the map changes). The stability of fixed points on switching manifolds is…

We show rational homological stability for the homotopy automorphisms and block diffeomorphims of iterated connected sums of products of spheres. The spheres can have different dimension, but need to satisfy a certain connectivity…

Within the general class of Asymptotically Anti-de Sitter spacetimes that are asymptotic to the A-de-S Schwarzschild metric, we give a simple positive mass theorem based on arguments from causal structure. A general result for all…

We consider arbitrary stationary and axisymmetric black holes in general relativity in $(d +1)$ dimensions (with $d \geq 3$) that satisfy the vacuum Einstein equation and have a non-degenerate horizon. We prove that the canonical energy of…

Using the positive energy theorem, we derive some constraints on static steller models in asymptotically flat spacetimes in a general setting without imposing spherical symmetry. We show that there exist no regular solutions under certain…

We prove a homological stability theorem for certain complements of symmetric spaces. This is a variant of a conjecture by Vakil and Matchett Wood for subspaces of $\mathrm{Sym}^n(X)$ where $X$ is an open manifold admitting a boundary. To…

We prove a Riemannian positive mass theorem for asymptotically flat spin manifolds with hypersurface singularities. Unlike earlier results, some components of the singular set may be mean-concave, provided that other components of the…

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 $\Sigma$. Moreover, we extend the local mass angular momenta…

A positive mass theorem for General Relativity Theory is proved. The proof is 4-dimensional in nature, and relies completely on arguments pertaining to causal structure, the basic idea being that positive energy-density focuses null…

We prove a homological stability theorem for the moduli spaces of manifolds diffeomorphic to g(S^n x S^n), provided n > 2. This generalises Harer's stability theorem for the homology of mapping class groups. Combined with previous work of…

We show the contractibility of spaces of invariant Riemannian metrics of positive scalar curvature on compact connected manifolds of dimension at least two, with and without boundary and equipped with compact Lie group actions. On manifolds…